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#### The Power of Logic 5th Edition by Howard-Snyder – Test Bank

6

Student: ___________________________________________________________________________

1. The predicate term of the conclusion in a standard form categorical syllogism is called the

A. major premise.

B. minor term.

C. middle premise.

D. major term.

2. Which of the following is not required in order for a categorical syllogism to be in standard form?

A. The premises and the conclusion are true.

B. The first premise contains the major term.

C. The second premise contains the minor term.

D. The conclusion is stated last.

3. The mood of a standard-form categorical syllogism whose major premise is universal affirmative, minor

premise is particular affirmative, and conclusion is particular affirmative would be

A. IAI.

B. IIA.

C. AII.

D. III.

4. The figure of a standard-form categorical syllogism whose middle term is the subject term of the major

premise and subject term of the minor premise would be

A. 1.

B. 2.

C. 3.

D. 4.

5. The form of a categorical syllogism is completely specified by

A. its mood.

B. its figure and mood.

C. its figure.

D. its mood, figure, and validity.

6. Which of the following categorical syllogisms is in standard form?

A. All dogs are mammals.

Cats are not dogs.

So, no cats are mammals.

B. All dogs are mammals.

No fish are mammals.

So, no dogs are fish.

C. Some mammals are small.

No whales are small.

So, no whales are mammals.

D. No whales are mammals.

Some whales are fish.

So, some fish are not mammals.

7. Identify the mood and figure of this standard-form categorical syllogism:

Some turncoats are not confederate soldiers.

No confederate soldiers are abolitionists.

So, some turncoats are abolitionists.

A. OEI-4

B. OEI-1

C. IEO-1

D. IAO-4

8. Identify the mood and figure of this standard-form categorical syllogism:

All excellent teachers are people who care about students.

All University 101 instructors are people who care about students.

So, all University 101 instructors are excellent teachers.

A. AAA-3

B. AAA-2

C. EEE-2

D. EEE-3

9. The Venn diagram representation of “All sailors are pirates” is which of the following?

A.

B.

C.

D.

10. The Venn diagram representation of “No sailors are pirates” is which of the following?

A.

B.

C.

D.

11. The Venn diagram representation of “Some sailors are pirates” is which of the following?

A.

B.

C.

D.

12. The Venn diagram representation of “Some sailors are not pirates” is which of the following?

A.

B.

C.

D.

13. Identify the Venn diagram representation of the following syllogism:

All minerals are rocks.

All diamonds are rocks.

So, all minerals are diamonds.

A.

B.

C.

D.

14. Identify the Venn diagram representation of the following syllogism:

Some ultraviolet radiation is not harmful to humans.

All ultraviolet radiation is a carcinogen.

So, some carcinogens are not harmful to humans.

A.

B.

C.

D.

15. Identify the Venn diagram representation of the following syllogism:

Some violinists are percussionists.

Some trombonists are percussionists.

So, some trombonists are violinists.

A.

B.

C.

D.

16. A categorical statement has existential import if and only if

A. it is a particular statement.

B. it implies that one of its terms denotes a nonempty class.

C. it implies that its subject term denotes a nonempty class.

D. it has importance for the nature of human existence.

17. Which of the following relations on the Square of Opposition is valid, according to modern categorical

logic?

A. contradictories

B. subcontraries

C. subalterns/subalternation

D. contraries

18. Which of the following immediate inferences is invalid according to modern categorical logic?

A. conversion

B. obversion

C. contraposition

D. contraposition by limitation

19. An enthymeme is an argument that

A. is found to be valid when tested with a Venn diagram.

B. has missing or unstated steps.

C. is a standard form categorical syllogism.

D. has the mood and figure AAA-1.

20. When supplying unstated steps, the principles of fairness and charity require that we

A. make the invalidity of the argument more apparent.

B. add only true (or at least plausible) steps.

C. supply premises that would improve the argument.

D. not make any critical remarks.

21. Which of the following is not a feature of standard-form sorites?

A. Each statement in the argument is a standard-form categorical statement.

B. Each premise (except the first) has a term in common with the immediately preceding premise.

C. The predicate term of the conclusion occurs in the last premise.

D. Each term appears twice—once in each of two different statements.

22. A sorites is

A. a chain of syllogisms in which the final conclusion is stated but the subconclusions are unstated.

B. an argument with an unstated premise or an unstated conclusion.

C. an argument comprised entirely of categorical statements.

D. a chain of inferences moving from the particular to the general.

23. When removing term-complements, which of the following is not a permissible change?

A. changing “No S are P” to “No P are S”

B. changing “All S are P” to “Some P are S”

C. changing “Some S are not P” to “Some non-P are not non-S”

D. changing “Some S are P” to “Some S are not non-P”

24. When removing term-complements, which of the following is a permissible change?

A. changing “Some S are P” to “Some non-P are non-S”

B. changing “All S are P” to “Some P are S”

C. changing “Some S are not P” to “Some non-P are not non-S”

D. changing “No S are P” to “Some S are not P”

25. A term is distributed in a statement when

A. it occurs in the subject position.

B. it occurs in the predicate position.

C. the statement says something about every member of its class.

D. the statement denies something about its class.

26. A fallacy of the undistributed middle is a violation of which of the following rules for evaluating

categorical syllogisms? In a valid standard-form categorical syllogism¼

A.

there are exactly three terms, and each term must be used with the same meaning throughout the

argument.

B. the middle term is distributed in at least one premise.

C. a term must be distributed in the premises if it is distributed in the conclusion.

D. if the conclusion is particular, then at least one of the premises must be particular.

27. A fallacy of illicit minor is a violation of which of the following rules for evaluating categorical

syllogisms? In a valid standard-form categorical syllogism¼

A.

there are exactly three terms, and each term must be used with the same meaning throughout the

argument.

B. the middle term is distributed in at least one premise.

C. a term must be distributed in the premises if it is distributed in the conclusion.

D. if the conclusion is particular, then at least one of the premises must be particular.

28. Which fallacy is committed by the following categorical syllogism?

All cats are soft and furry animals.

Some amphibians are not soft and furry animals.

So, no cats are amphibians.

A. fallacy of the undistributed middle

B. fallacy of the illicit middle

C. fallacy of the illicit major

D. fallacy of the illicit minor

29. The predicate term of the conclusion is the major term of a standard form categorical syllogism.

True False

30. The term that occurs once in each premise is called the bridge term.

True False

31. The minor term is the subject term of the conclusion.

True False

32. In a standard-form categorical syllogism, the minor premise always comes first.

True False

33. In a standard-form categorical syllogism, the conclusion always comes last.

True False

34. The figure of a standard-form categorical syllogism indicates the position of the middle term.

True False

35. The mood of a standard-form categorical syllogism is an indicator of the position of the middle term in

the premises.

True False

36. Two different categorical syllogisms cannot have the same mood and figure.

True False

37. The form of a categorical syllogism is completely specified by its mood and figure.

True False

38. To show that an area of a Venn diagram is empty, we use an “x” in that area.

True False

39. When an area of a Venn diagram is shaded, it indicates that there is at least one thing in that area.

True False

40. When a syllogism contains both a universal and a particular premise, you should always diagram the

universal first.

True False

41. A categorical statement has existential import when (and only when) it implies that its subject terms only

denote classes that have at least one member (i.e., are nonempty).

True False

42. Aristotelian and modern logicians agree that universal categorical statements have existential import.

True False

43. According to modern logicians, “All elves are people with infrared vision” is equivalent to “If anything is

an elf, then it is a person with infrared vision.”

True False

44. The only relationship on the Square of Opposition that both Aristotelian and modern logicians accept is

contradictories.

True False

45. An enthymeme is an argument with a true conclusion.

True False

46. All enthymemes are valid.

True False

47. When forced to choose between adding a false premise and making an enthymeme clearly invalid, we

adopt the practice of adding a false premise and thereby making the syllogism valid.

True False

48. A sorites is a chain of syllogisms in which the final conclusion is stated but the subconclusions are

unstated.

True False

49. In a standard form sorites, the subject term of the conclusion must occur in the first premise.

True False

50. Evaluating the validity of a sorites requires that we identify all its subconclusions.

True False

51. When reducing the number of terms (removing term complements) in a categorical syllogism, we are not

permitted to use conversion by limitation nor contraposition by limitation.

True False

52. The only requirement when removing term complements is that the changes we make to each statement

must produce a logically equivalent statement.

True False

53. A term is distributed in a categorical statement if the statement says something about every member of

the class that term denotes.

True False

54. In “Some dogs are mammals,” the subject term is distributed.

True False

55. In a universal negative statement, both terms are distributed.

True False

56. In a valid standard-form categorical syllogism, the middle term must be distributed in at least one

premise.

True False

57. Any categorical syllogism with two negative premises is invalid.

True False

58. Any categorical syllogism with two affirmative premises is valid.

True False

59. From the standpoint of modern logic, a valid standard-form categorical syllogism with a particular

conclusion can have two universal premises.

True False

60. Rewrite the following argument as a standard-form categorical syllogism; then identify its mood and

figure: All hyperventilating iguanas are bungee-jumpers since all bungee-jumpers are pencil-pushers and

some pencil-pushers are hyperventilating iguanas.

61. Rewrite the following argument as a standard-form categorical syllogism; then identify its mood and

figure: No drowsy dromedaries are prized prodigies since all prized prodigies are shameless sheiks and no

shameless sheiks are drowsy dromedaries.

62. Rewrite the following argument as a standard-form categorical syllogism; then identify its mood and

figure: No tragic actors are idiots. But some comedians are not idiots. So, some comedians are not tragic

actors.

63. Rewrite the following argument as a standard-form categorical syllogism; then identify its mood and

figure: No coal tar derivatives are nourishing foods, because all artificial dyes are coal tar derivatives and

no artificial dyes are nourishing foods.

64. Rewrite the following argument as a standard-form categorical syllogism; then identify its mood and

figure: Some spaniels are not good hunters, though all spaniels are gentle dogs. Thus, no gentle dogs are

good hunters.

65. Rewrite the following argument as a standard-form categorical syllogism; then identify its mood and

figure: All professional wrestlers are good actors, because some good actors are not powerful athletes and

all professional wrestlers are powerful athletes.

66. Rewrite the following argument as a standard-form categorical syllogism; then identify its mood and

figure: All patriotic citizens are mindless followers of the government, and all soldiers are mindless

followers of the government, so all soldiers are patriotic citizens.

67. Rewrite the following argument as a standard-form categorical syllogism; then identify its mood and

figure: Since some science professors are absent-minded persons and all philosophers are absent-minded

persons, some scientists are not philosophers.

68. Rewrite the following argument as a standard-form categorical syllogism; then identify its mood and

figure: No knights are shrubberies, since no shrubberies are jousters and all jousters are knights.

69. Rewrite the following argument as a standard-form categorical syllogism; then identify its mood and

figure: Whereas all Klingon warriors are ferocious opponents and some Klingon warriors are not male, it

must be that some ferocious opponents are not males.

70. Rewrite the following argument as a standard-form categorical syllogism; then identify its mood and

figure: Some tax-exempt organizations are religious associations and no tax-exempt organizations are

profitable businesses. Thus, some religious associations are not profitable businesses.

71. Rewrite the following argument as a standard-form categorical syllogism; then identify its mood and

figure: Since all aardvarks are CB radio operators, and no CB radio operators are Olympic champions, no

Olympic champions are aardvarks.

72. Rewrite the following argument as a standard-form categorical syllogism; then identify its mood and

figure: Some Tibetan monks are bookstore junkies, because no Ronald Reagan movie fans are bookstore

junkies and some Tibetan monks are Ronald Reagan movie fans.

73. Rewrite the following argument as a standard-form categorical syllogism; then identify its mood and

figure: All cartographers are Martians from outer space, and some cartographers are not agents for the

CIA, whence it follows that some agents for the CIA are not Martians from outer space.

74. Rewrite the following argument as a standard-form categorical syllogism; then identify its mood and

figure: Some Swedish water volleyball team members are not beer drinkers, because some molecular

biologists are Swedish water volleyball team members and some molecular biologists are not beer

drinkers.

75. The following categorical argument form has more than three terms: “Some non-P are non-M. All non-S

are M. So, some S are not P.” Reduce the terms to three by removing term-complements via applications

of conversion, obversion, and/or contraposition.

76. The following categorical argument form has more than three terms: “No non-M are P. Some S are non-

M. So, no S are non-P.” Reduce the terms to three by removing term-complements via applications of

conversion, obversion, and/or contraposition.

77. The following categorical argument form has more than three terms: “No non-P are non-M. Some M are

non-S. So, some S are P.” Reduce the terms to three by removing term-complements via applications of

conversion, obversion, and/or contraposition.

78. The following categorical argument form has more than three terms: “All non-P are M. Some S are non-

M. So, no non-S are P.” Reduce the terms to three by removing term-complements via applications of

conversion, obversion, and/or contraposition.

79. The following categorical argument form has more than three terms: “All P are M. Some non-S are M.

So, no non-S are non-P.” Reduce the terms to three by removing term-complements via applications of

conversion, obversion, and/or contraposition.

80. Which of the five rules for evaluating syllogisms can you use to determine whether the following form is

valid?

All M are P.

No S are M.

So, no S are P.

81. Which of the five rules for evaluating syllogisms can you use to determine whether the following form is

valid?

All M are P.

All M are S.

Some S are not P.

82. Which of the five rules for evaluating syllogisms can you use to determine whether the following form is

valid?

No M are P.

No S are M.

All S are P.

83. Which of the five rules for evaluating syllogisms can you use to determine whether the following form is

valid?

All P are M.

Some S are M.

So, some S are not P.

84. Which of the five rules for evaluating syllogisms can you use to determine whether the following form is

valid?

All M are P.

All M are S.

So, all S are P.

85. Put the following categorical syllogism into standard form and identify its mood and figure.

No Romulans are Members of the Federation. This is because all Members of the federation are peaceful

races and all Romulans are peaceful races.

86. Put the following categorical syllogism into standard form and identify its mood and figure.

Whereas all Klingon warriors are ferocious opponents and some Klingon warriors are not male, it must be

that some ferocious opponents are not males.

87. Put the following categorical syllogism into standard form and identify its mood and figure.

No Starships are Ferengi inventions because all Warp-capable ships are Starships and no Ferengi

inventions are Warp-capable ships.

88. Put the following categorical syllogism into standard form and identify its mood and figure.

Because some Makhi are Lieutenants in the Federation and no criminals are Makhi, some Lieutenants in

the Federation are not criminals.

89. Put the following categorical syllogism into standard form and identify its mood and figure.

Some shuttle-craft are not ships with shields because some scientific vessels are shuttle-craft and some

scientific vessels are not ships with shields.

90. Put the following categorical syllogism into standard form and identify its mood and figure.

All snakes are cold-blooded animals, so some snakes are egg-layers since some cold-blooded animals are

egg-layers.

91. Put the following categorical syllogism into standard form and identify its mood and figure.

No tragic actors are idiots. But some comedians are not idiots. So, some comedians are not tragic

actors.

92. Put the following categorical syllogism into standard form and identify its mood and figure.

Some diamonds are not precious stones and some carbon compounds are not diamonds. Thus, some

carbon compounds are not precious stones.

93. Put the following categorical syllogism into standard form and identify its mood and figure.

No coal tar derivatives are nourishing foods, because all artificial dyes are coal tar derivatives and no

artificial dyes are nourishing foods.

94. Put the following categorical syllogism into standard form and identify its mood and figure.

Some parrots are not pests. All parrots are pets. Thus, no pets are pests.

95. Put the following categorical syllogism into standard form and identify its mood and figure.

All criminal actions are wicked deeds. All prosecutions for murder are criminal actions. Thus, all

prosecutions for murder are wicked deeds.

96. Put the following categorical syllogism into standard form and identify its mood and figure.

No writers of lewd and sensational articles are honest and decent citizens, but some journalists are not

writers of lewd and sensational articles; consequently some journalists are honest and decent citizens.

97. Put the following categorical syllogism into standard form and identify its mood and figure.

Some spaniels are not good hunters, though all spaniels are gentle dogs. Thus, no gentle dogs are good

hunters.

98. Put the following categorical syllogism into standard form and identify its mood and figure.

All professional wrestlers are good actors, because some good actors are not powerful athletes and all

professional wrestlers are powerful athletes.

99. Put the following categorical syllogism into standard form and identify its mood and figure.

All storm troopers are metalheads, so some storm troopers are not ballet afficionados, since some ballet

afficionados are metalheads.

100.Put the following categorical syllogism into standard form and identify its mood and figure.

No reticulocytes are leukocytes, but all phagocytic cells are reticulocytes. Whence it follows that no

phagocytic cells are leukocytes.

101.Put the following categorical syllogism into standard form and identify its mood and figure.

Some calyculated planets are high-orbiting satellites. But some zoantharians are calyculated planets, since

some high-orbiting satellites are zoantharians.

102.Put the following categorical syllogism into standard form and identify its mood and figure.

No Shoshoneans are Tylezian mud-dobbers, but all Shoshoneans are quixotic members of the Uto-

Aztecan phylum. So, some Tylezian mud-dobbers are quixotic members of the Uto-Aztecan phylum.

103.Put the following categorical syllogism into standard form and identify its mood and figure.

Some Necromonicons are Talmudic doctrines, given that all Linneaen manuscripts are Necromonicons

and some Talmudic doctrines are Linneaen manuscripts.

104.Put the following categorical syllogism into standard form and identify its mood and figure.

Since no hobbits are grand wizards and some grand wizards are members of the Circle of Seven, it

follows that some members of the Circle of Seven are not hobbits.

105.Identify the missing step in the following argument (remember the principles of charity and fairness!

). Then put the argument into standard form. To cut down on writing, use capital letters to abbreviate

English terms.

Because all whales are mammals, at least some aquatic animals are mammals.

106.Identify the missing step in the following argument (remember the principles of charity and fairness!

). Then put the argument into standard form. To cut down on writing, use capital letters to abbreviate

English terms.

No fallacies are valid arguments, since no valid arguments are mistakes in reasoning.

107.Identify the missing step in the following argument (remember the principles of charity and fairness!

). Then put the argument into standard form. To cut down on writing, use capital letters to abbreviate

English terms.

Since all chickens are egg-layers, it follows that no chickens are mammals.

108.Identify the missing step in the following argument (remember the principles of charity and fairness!

). Then put the argument into standard form. To cut down on writing, use capital letters to abbreviate

English terms.

All psychics are frauds, because all psychics are people who make false claims about their abilities.

109.Identify the missing step in the following argument (remember the principles of charity and fairness!

). Then put the argument into standard form. To cut down on writing, use capital letters to abbreviate

English terms.

It must be that some tabloid reporters are gossipmongers because all overzealous journalists are tabloid

reporters.

110.Identify the missing step in the following argument (remember the principles of charity and fairness!

). Then put the argument into standard form. To cut down on writing, use capital letters to abbreviate

English terms.

Some arguments are sound arguments because some arguments are valid arguments and all valid

arguments are sound arguments.

6 Key

1. The predicate term of the conclusion in a standard form categorical syllogism is called the

A. major premise.

B. minor term.

C. middle premise.

D. major term.

Howard – Chapter 06 #1

Subject area: 6.1 Standard Form, Mood, and Figure

2. Which of the following is not required in order for a categorical syllogism to be in standard form?

A. The premises and the conclusion are true.

B. The first premise contains the major term.

C. The second premise contains the minor term.

D. The conclusion is stated last.

Howard – Chapter 06 #2

Subject area: 6.1 Standard Form, Mood, and Figure

3. The mood of a standard-form categorical syllogism whose major premise is universal affirmative,

minor premise is particular affirmative, and conclusion is particular affirmative would be

A. IAI.

B. IIA.

C. AII.

D. III.

Howard – Chapter 06 #3

Subject area: 6.1 Standard Form, Mood, and Figure

4. The figure of a standard-form categorical syllogism whose middle term is the subject term of the

major premise and subject term of the minor premise would be

A. 1.

B. 2.

C. 3.

D. 4.

Howard – Chapter 06 #4

Subject area: 6.1 Standard Form, Mood, and Figure

5. The form of a categorical syllogism is completely specified by

A. its mood.

B. its figure and mood.

C. its figure.

D. its mood, figure, and validity.

Howard – Chapter 06 #5

Subject area: 6.1 Standard Form, Mood, and Figure

6. Which of the following categorical syllogisms is in standard form?

A. All dogs are mammals.

Cats are not dogs.

So, no cats are mammals.

B. All dogs are mammals.

No fish are mammals.

So, no dogs are fish.

C. Some mammals are small.

No whales are small.

So, no whales are mammals.

D. No whales are mammals.

Some whales are fish.

So, some fish are not mammals.

Howard – Chapter 06 #6

Subject area: 6.1 Standard Form, Mood, and Figure

7. Identify the mood and figure of this standard-form categorical syllogism:

Some turncoats are not confederate soldiers.

No confederate soldiers are abolitionists.

So, some turncoats are abolitionists.

A. OEI-4

B. OEI-1

C. IEO-1

D. IAO-4

Howard – Chapter 06 #7

Subject area: 6.1 Standard Form, Mood, and Figure

8. Identify the mood and figure of this standard-form categorical syllogism:

All excellent teachers are people who care about students.

All University 101 instructors are people who care about students.

So, all University 101 instructors are excellent teachers.

A. AAA-3

B. AAA-2

C. EEE-2

D. EEE-3

Howard – Chapter 06 #8

Subject area: 6.1 Standard Form, Mood, and Figure

9. The Venn diagram representation of “All sailors are pirates” is which of the following?

A.

B.

C.

D.

Howard – Chapter 06 #9

Subject area: 6.2 Venn Diagrams and Categorical Statements

10. The Venn diagram representation of “No sailors are pirates” is which of the following?

A.

B.

C.

D.

Howard – Chapter 06 #10

Subject area: 6.2 Venn Diagrams and Categorical Statements

11. The Venn diagram representation of “Some sailors are pirates” is which of the following?

A.

B.

C.

D.

Howard – Chapter 06 #11

Subject area: 6.2 Venn Diagrams and Categorical Statements

12. The Venn diagram representation of “Some sailors are not pirates” is which of the following?

A.

B.

C.

D.

Howard – Chapter 06 #12

Subject area: 6.2 Venn Diagrams and Categorical Statements

13. Identify the Venn diagram representation of the following syllogism:

All minerals are rocks.

All diamonds are rocks.

So, all minerals are diamonds.

A.

B.

C.

D.

Howard – Chapter 06 #13

Subject area: 6.3 Venn Diagrams and Categorical Syllogisms

14. Identify the Venn diagram representation of the following syllogism:

Some ultraviolet radiation is not harmful to humans.

All ultraviolet radiation is a carcinogen.

So, some carcinogens are not harmful to humans.

A.

B.

C.

D.

Howard – Chapter 06 #14

Subject area: 6.3 Venn Diagrams and Categorical Syllogisms

15. Identify the Venn diagram representation of the following syllogism:

Some violinists are percussionists.

Some trombonists are percussionists.

So, some trombonists are violinists.

A.

B.

C.

D.

Howard – Chapter 06 #15

Subject area: 6.3 Venn Diagrams and Categorical Syllogisms

16. A categorical statement has existential import if and only if

A. it is a particular statement.

B. it implies that one of its terms denotes a nonempty class.

C. it implies that its subject term denotes a nonempty class.

D. it has importance for the nature of human existence.

Howard – Chapter 06 #16

Subject area: 6.4 The Modern Square of Opposition

17. Which of the following relations on the Square of Opposition is valid, according to modern

categorical logic?

A. contradictories

B. subcontraries

C. subalterns/subalternation

D. contraries

Howard – Chapter 06 #17

Subject area: 6.4 The Modern Square of Opposition

18. Which of the following immediate inferences is invalid according to modern categorical logic?

A. conversion

B. obversion

C. contraposition

D. contraposition by limitation

Howard – Chapter 06 #18

Subject area: The Modern Square of Opposition

19. An enthymeme is an argument that

A. is found to be valid when tested with a Venn diagram.

B. has missing or unstated steps.

C. is a standard form categorical syllogism.

D. has the mood and figure AAA-1.

Howard – Chapter 06 #19

Subject area: 6.5 Enthymemes

20. When supplying unstated steps, the principles of fairness and charity require that we

A. make the invalidity of the argument more apparent.

B. add only true (or at least plausible) steps.

C. supply premises that would improve the argument.

D. not make any critical remarks.

Howard – Chapter 06 #20

Subject area: 6.5 Enthymemes

21. Which of the following is not a feature of standard-form sorites?

A. Each statement in the argument is a standard-form categorical statement.

B. Each premise (except the first) has a term in common with the immediately preceding premise.

C. The predicate term of the conclusion occurs in the last premise.

D. Each term appears twice—once in each of two different statements.

Howard – Chapter 06 #21

Subject area: 6.6 Sorites and Removing Term-Complements

22. A sorites is

A. a chain of syllogisms in which the final conclusion is stated but the subconclusions are unstated.

B. an argument with an unstated premise or an unstated conclusion.

C. an argument comprised entirely of categorical statements.

D. a chain of inferences moving from the particular to the general.

Howard – Chapter 06 #22

Subject area: 6.6 Sorites and Removing Term-Complements

23. When removing term-complements, which of the following is not a permissible change?

A. changing “No S are P” to “No P are S”

B. changing “All S are P” to “Some P are S”

C. changing “Some S are not P” to “Some non-P are not non-S”

D. changing “Some S are P” to “Some S are not non-P”

Howard – Chapter 06 #23

Subject area: 6.6 Sorites and Removing Term-Complements

24. When removing term-complements, which of the following is a permissible change?

A. changing “Some S are P” to “Some non-P are non-S”

B. changing “All S are P” to “Some P are S”

C. changing “Some S are not P” to “Some non-P are not non-S”

D. changing “No S are P” to “Some S are not P”

Howard – Chapter 06 #24

Subject area: 6.6 Sorites and Removing Term-Complements

25. A term is distributed in a statement when

A. it occurs in the subject position.

B. it occurs in the predicate position.

C. the statement says something about every member of its class.

D. the statement denies something about its class.

Howard – Chapter 06 #25

Subject area: 6.7 Rules for Evaluating Syllogisms

26. A fallacy of the undistributed middle is a violation of which of the following rules for evaluating

categorical syllogisms? In a valid standard-form categorical syllogism¼

A.

there are exactly three terms, and each term must be used with the same meaning throughout the

argument.

B. the middle term is distributed in at least one premise.

C. a term must be distributed in the premises if it is distributed in the conclusion.

D. if the conclusion is particular, then at least one of the premises must be particular.

Howard – Chapter 06 #26

Subject area: 6.7 Rules for Evaluating Syllogisms

27. A fallacy of illicit minor is a violation of which of the following rules for evaluating categorical

syllogisms? In a valid standard-form categorical syllogism¼

A.

there are exactly three terms, and each term must be used with the same meaning throughout the

argument.

B. the middle term is distributed in at least one premise.

C. a term must be distributed in the premises if it is distributed in the conclusion.

D. if the conclusion is particular, then at least one of the premises must be particular.

Howard – Chapter 06 #27

Subject area: 6.7 Rules for Evaluating Syllogisms

28. Which fallacy is committed by the following categorical syllogism?

All cats are soft and furry animals.

Some amphibians are not soft and furry animals.

So, no cats are amphibians.

A. fallacy of the undistributed middle

B. fallacy of the illicit middle

C. fallacy of the illicit major

D. fallacy of the illicit minor

Howard – Chapter 06 #28

Subject area: 6.7 Rules for Evaluating Syllogisms

29. The predicate term of the conclusion is the major term of a standard form categorical syllogism.

TRUE

Howard – Chapter 06 #29

Subject area: 6.1 Standard Form, Mood, and Figure

30. The term that occurs once in each premise is called the bridge term.

FALSE

Howard – Chapter 06 #30

Subject area: 6.1 Standard Form, Mood, and Figure

31. The minor term is the subject term of the conclusion.

TRUE

Howard – Chapter 06 #31

Subject area: 6.1 Standard Form, Mood, and Figure

32. In a standard-form categorical syllogism, the minor premise always comes first.

FALSE

Howard – Chapter 06 #32

Subject area: 6.1 Standard Form, Mood, and Figure

33. In a standard-form categorical syllogism, the conclusion always comes last.

TRUE

Howard – Chapter 06 #33

34. The figure of a standard-form categorical syllogism indicates the position of the middle term.

TRUE

Howard – Chapter 06 #34

Subject area: 6.1 Standard Form, Mood, and Figure

35. The mood of a standard-form categorical syllogism is an indicator of the position of the middle term in

the premises.

FALSE

Howard – Chapter 06 #35

Subject area: 6.1 Standard Form, Mood, and Figure

36. Two different categorical syllogisms cannot have the same mood and figure.

FALSE

Howard – Chapter 06 #36

Subject area: 6.1 Standard Form, Mood, and Figure

37. The form of a categorical syllogism is completely specified by its mood and figure.

TRUE

Howard – Chapter 06 #37

Subject area: 6.1 Standard Form, Mood, and Figure

38. To show that an area of a Venn diagram is empty, we use an “x” in that area.

FALSE

Howard – Chapter 06 #38

Subject area: 6.2 Venn Diagrams and Categorical Statements

39. When an area of a Venn diagram is shaded, it indicates that there is at least one thing in that area.

FALSE

Howard – Chapter 06 #39

Subject area: 6.2 Venn Diagrams and Categorical Statements

40. When a syllogism contains both a universal and a particular premise, you should always diagram the

universal first.

TRUE

Howard – Chapter 06 #40

Subject area: 6.3 Venn Diagrams and Categorical Syllogisms

41. A categorical statement has existential import when (and only when) it implies that its subject terms

only denote classes that have at least one member (i.e., are nonempty).

TRUE

Howard – Chapter 06 #41

Subject area: 6.4 The Modern Square of Opposition

42. Aristotelian and modern logicians agree that universal categorical statements have existential

import.

FALSE

Howard – Chapter 06 #42

Subject area: 6.4 The Modern Square of Opposition

43. According to modern logicians, “All elves are people with infrared vision” is equivalent to “If

anything is an elf, then it is a person with infrared vision.”

TRUE

Howard – Chapter 06 #43

Subject area: 6.4 The Modern Square of Opposition

44. The only relationship on the Square of Opposition that both Aristotelian and modern logicians accept

is contradictories.

TRUE

Howard – Chapter 06 #44

Subject area: 6.4 The Modern Square of Opposition

45. An enthymeme is an argument with a true conclusion.

FALSE

Howard – Chapter 06 #45

Subject area: 6.5 Enthymemes

46. All enthymemes are valid.

FALSE

Howard – Chapter 06 #46

Subject area: 6.5 Enthymemes

47. When forced to choose between adding a false premise and making an enthymeme clearly invalid, we

adopt the practice of adding a false premise and thereby making the syllogism valid.

TRUE

Howard – Chapter 06 #47

Subject area: 6.5 Enthymemes

48. A sorites is a chain of syllogisms in which the final conclusion is stated but the subconclusions are

unstated.

TRUE

Howard – Chapter 06 #48

Subject area: 6.6 Sorites and Removing Term-Complements

49. In a standard form sorites, the subject term of the conclusion must occur in the first premise.

FALSE

Howard – Chapter 06 #49

Subject area: 6.6 Sorites and Removing Term-Complements

50. Evaluating the validity of a sorites requires that we identify all its subconclusions.

TRUE

Howard – Chapter 06 #50

Subject area: 6.6 Sorites and Removing Term-Complements

51. When reducing the number of terms (removing term complements) in a categorical syllogism, we are

not permitted to use conversion by limitation nor contraposition by limitation.

TRUE

Howard – Chapter 06 #51

Subject area: 6.6 Sorites and Removing Term-Complements

52. The only requirement when removing term complements is that the changes we make to each

statement must produce a logically equivalent statement.

TRUE

Howard – Chapter 06 #52

Subject area: 6.6 Sorites and Removing Term-Complements

53. A term is distributed in a categorical statement if the statement says something about every member of

the class that term denotes.

TRUE

Howard – Chapter 06 #53

Subject area: 6.7 Rules for Evaluating Syllogisms

54. In “Some dogs are mammals,” the subject term is distributed.

FALSE

Howard – Chapter 06 #54

Subject area: 6.7 Rules for Evaluating Syllogisms

55. In a universal negative statement, both terms are distributed.

TRUE

Howard – Chapter 06 #55

Subject area: 6.7 Rules for Evaluating Syllogisms

56. In a valid standard-form categorical syllogism, the middle term must be distributed in at least one

premise.

TRUE

Howard – Chapter 06 #56

Subject area: 6.7 Rules for Evaluating Syllogisms

57. Any categorical syllogism with two negative premises is invalid.

TRUE

Howard – Chapter 06 #57

Subject area: 6.7 Rules for Evaluating Syllogisms

58. Any categorical syllogism with two affirmative premises is valid.

FALSE

Howard – Chapter 06 #58

Subject area: 6.7 Rules for Evaluating Syllogisms

59. From the standpoint of modern logic, a valid standard-form categorical syllogism with a particular

conclusion can have two universal premises.

FALSE

Howard – Chapter 06 #59

Subject area: 6.7 Rules for Evaluating Syllogisms

60. Rewrite the following argument as a standard-form categorical syllogism; then identify its mood and

figure: All hyperventilating iguanas are bungee-jumpers since all bungee-jumpers are pencil-pushers

and some pencil-pushers are hyperventilating iguanas.

AIA-4

Howard – Chapter 06 #60

Subject area: Putting syllogisms into standard form

61. Rewrite the following argument as a standard-form categorical syllogism; then identify its mood and

figure: No drowsy dromedaries are prized prodigies since all prized prodigies are shameless sheiks

and no shameless sheiks are drowsy dromedaries.

AEE-4

Howard – Chapter 06 #61

Subject area: Putting syllogisms into standard form

62. Rewrite the following argument as a standard-form categorical syllogism; then identify its mood and

figure: No tragic actors are idiots. But some comedians are not idiots. So, some comedians are not

tragic actors.

EOO-2

Howard – Chapter 06 #62

Subject area: Putting syllogisms into standard form

63. Rewrite the following argument as a standard-form categorical syllogism; then identify its mood and

figure: No coal tar derivatives are nourishing foods, because all artificial dyes are coal tar derivatives

and no artificial dyes are nourishing foods.

EAE-3

Howard – Chapter 06 #63

Subject area: Putting syllogisms into standard form

64. Rewrite the following argument as a standard-form categorical syllogism; then identify its mood and

figure: Some spaniels are not good hunters, though all spaniels are gentle dogs. Thus, no gentle dogs

are good hunters.

OAE-3

Howard – Chapter 06 #64

Subject area: Putting syllogisms into standard form

65. Rewrite the following argument as a standard-form categorical syllogism; then identify its mood and

figure: All professional wrestlers are good actors, because some good actors are not powerful athletes

and all professional wrestlers are powerful athletes.

OAA-2

Howard – Chapter 06 #65

Subject area: Putting syllogisms into standard form

66. Rewrite the following argument as a standard-form categorical syllogism; then identify its mood and

figure: All patriotic citizens are mindless followers of the government, and all soldiers are mindless

followers of the government, so all soldiers are patriotic citizens.

AAA-2

Howard – Chapter 06 #66

Subject area: Putting syllogisms into standard form

67. Rewrite the following argument as a standard-form categorical syllogism; then identify its mood and

figure: Since some science professors are absent-minded persons and all philosophers are absentminded

persons, some scientists are not philosophers.

AIO-2

Howard – Chapter 06 #67

Subject area: Putting syllogisms into standard form

68. Rewrite the following argument as a standard-form categorical syllogism; then identify its mood and

figure: No knights are shrubberies, since no shrubberies are jousters and all jousters are knights.

EAE-4

Howard – Chapter 06 #68

Subject area: Putting syllogisms into standard form

69. Rewrite the following argument as a standard-form categorical syllogism; then identify its mood and

figure: Whereas all Klingon warriors are ferocious opponents and some Klingon warriors are not

male, it must be that some ferocious opponents are not males.

OAO-3

Howard – Chapter 06 #69

Subject area: Putting syllogisms into standard form

70. Rewrite the following argument as a standard-form categorical syllogism; then identify its mood and

figure: Some tax-exempt organizations are religious associations and no tax-exempt organizations are

profitable businesses. Thus, some religious associations are not profitable businesses.

EIO-3

Howard – Chapter 06 #70

Subject area: Putting syllogisms into standard form

71. Rewrite the following argument as a standard-form categorical syllogism; then identify its mood and

figure: Since all aardvarks are CB radio operators, and no CB radio operators are Olympic champions,

no Olympic champions are aardvarks.

AEE-4

Howard – Chapter 06 #71

Subject area: Putting syllogisms into standard form

72. Rewrite the following argument as a standard-form categorical syllogism; then identify its mood

and figure: Some Tibetan monks are bookstore junkies, because no Ronald Reagan movie fans are

bookstore junkies and some Tibetan monks are Ronald Reagan movie fans.

EII-1

Howard – Chapter 06 #72

Subject area: Putting syllogisms into standard form

73. Rewrite the following argument as a standard-form categorical syllogism; then identify its mood and

figure: All cartographers are Martians from outer space, and some cartographers are not agents for the

CIA, whence it follows that some agents for the CIA are not Martians from outer space.

AOO-3

Howard – Chapter 06 #73

Subject area: Putting syllogisms into standard form

74. Rewrite the following argument as a standard-form categorical syllogism; then identify its mood and

figure: Some Swedish water volleyball team members are not beer drinkers, because some molecular

biologists are Swedish water volleyball team members and some molecular biologists are not beer

drinkers.

Answers will vary

Howard – Chapter 06 #74

Subject area: Putting syllogisms into standard form

75. The following categorical argument form has more than three terms: “Some non-P are non-M. All

non-S are M. So, some S are not P.” Reduce the terms to three by removing term-complements via

applications of conversion, obversion, and/or contraposition.

Some non-P are non-M.

No non-S are non-M. (obversion)

So, some non-P are not non-S. (contraposition)

Howard – Chapter 06 #75

Subject area: Removing term-complements

76. The following categorical argument form has more than three terms: “No non-M are P. Some S

are non-M. So, no S are non-P.” Reduce the terms to three by removing term-complements via

applications of conversion, obversion, and/or contraposition.

All P are M. (conversion, obversion)

Some S are not M. (obversion)

So, all S are P. (obversion)

Or:

No non-M are P.

Some S are non-M.

So, all S are P. (obversion)

Howard – Chapter 06 #76

Subject area: Removing term-complements

77. The following categorical argument form has more than three terms: “No non-P are non-M. Some

M are non-S. So, some S are P.” Reduce the terms to three by removing term-complements via

applications of conversion, obversion, and/or contraposition.

All non-P are M. (obversion)

Some M are not S. (obversion)

So, some S are not non-P. (obversion)

Howard – Chapter 06 #77

Subject area: Removing term-complements

78. The following categorical argument form has more than three terms: “All non-P are M. Some S

are non-M. So, no non-S are P.” Reduce the terms to three by removing term-complements via

applications of conversion, obversion, and/or contraposition.

No non-P are non-M. (obversion)

Some non-M are not non-S. (conversion, obversion)

So, all non-S are non-P. (obversion)

Howard – Chapter 06 #78

Subject area: Removing term-complements

79. The following categorical argument form has more than three terms: “All P are M. Some non-S are M.

So, no non-S are non-P.” Reduce the terms to three by removing term-complements via applications

of conversion, obversion, and/or contraposition.

All non-M are non-P. (contraposition)

Some non-S are not non-M. (obversion)

So, no non-S are non-P.

Or:

All P are M.

Some non-S are M.

So, all non-S are P. (obversion)

Howard – Chapter 06 #79

Subject area: Removing term-complements

80. Which of the five rules for evaluating syllogisms can you use to determine whether the following form

is valid?

All M are P.

No S are M.

So, no S are P.

Rule 3 (fallacy of illicit major)

Howard – Chapter 06 #80

Subject area: Rules for evaluating syllogisms

81. Which of the five rules for evaluating syllogisms can you use to determine whether the following form

is valid?

All M are P.

All M are S.

Some S are not P.

Rules 4 and 5

Howard – Chapter 06 #81

Subject area: Rules for evaluating syllogisms

82. Which of the five rules for evaluating syllogisms can you use to determine whether the following form

is valid?

No M are P.

No S are M.

All S are P.

Rule 4

Howard – Chapter 06 #82

Subject area: Rules for evaluating syllogisms

83. Which of the five rules for evaluating syllogisms can you use to determine whether the following form

is valid?

All P are M.

Some S are M.

So, some S are not P.

Rules 2 (fallacy of undistributed middle) and 4

Howard – Chapter 06 #83

Subject area: Rules for evaluating syllogisms

84. Which of the five rules for evaluating syllogisms can you use to determine whether the following form

is valid?

All M are P.

All M are S.

So, all S are P.

Rule 3 (fallacy of illicit minor)

Howard – Chapter 06 #84

Subject area: Rules for evaluating syllogisms

85. Put the following categorical syllogism into standard form and identify its mood and figure.

No Romulans are Members of the Federation. This is because all Members of the federation are

peaceful races and all Romulans are peaceful races.

AAE-2, invalid

Howard – Chapter 06 #85

Subject area: Venn diagrams and categorical syllogisms

86. Put the following categorical syllogism into standard form and identify its mood and figure.

Whereas all Klingon warriors are ferocious opponents and some Klingon warriors are not male, it

must be that some ferocious opponents are not males.

OAO-e, valid

Howard – Chapter 06 #86

Subject area: Venn diagrams and categorical syllogisms

87. Put the following categorical syllogism into standard form and identify its mood and figure.

No Starships are Ferengi inventions because all Warp-capable ships are Starships and no Ferengi

inventions are Warp-capable ships.

EAE-4, invalid

Howard – Chapter 06 #87

Subject area: Venn diagrams and categorical syllogisms

88. Put the following categorical syllogism into standard form and identify its mood and figure.

Because some Makhi are Lieutenants in the Federation and no criminals are Makhi, some Lieutenants

in the Federation are not criminals.

EIO-4, valid

Howard – Chapter 06 #88

Subject area: Venn diagrams and categorical syllogisms

89. Put the following categorical syllogism into standard form and identify its mood and figure.

Some shuttle-craft are not ships with shields because some scientific vessels are shuttle-craft and some

scientific vessels are not ships with shields.

OIO-2, invalid

Howard – Chapter 06 #89

Subject area: Venn diagrams and categorical syllogisms

90. Put the following categorical syllogism into standard form and identify its mood and figure.

All snakes are cold-blooded animals, so some snakes are egg-layers since some cold-blooded animals

are egg-layers.

IAI-1, invalid

Howard – Chapter 06 #90

Subject area: Venn diagrams and categorical syllogisms

91. Put the following categorical syllogism into standard form and identify its mood and figure.

No tragic actors are idiots. But some comedians are not idiots. So, some comedians are not tragic

actors.

EOO-2, invalid

Howard – Chapter 06 #91

Subject area: Venn diagrams and categorical syllogisms

92. Put the following categorical syllogism into standard form and identify its mood and figure.

Some diamonds are not precious stones and some carbon compounds are not diamonds. Thus, some

carbon compounds are not precious stones.

OOI-1, invalid

Howard – Chapter 06 #92

Subject area: Venn diagrams and categorical syllogisms

93. Put the following categorical syllogism into standard form and identify its mood and figure.

No coal tar derivatives are nourishing foods, because all artificial dyes are coal tar derivatives and no

artificial dyes are nourishing foods.

EAE-3, invalid

Howard – Chapter 06 #93

Subject area: Venn diagrams and categorical syllogisms

94. Put the following categorical syllogism into standard form and identify its mood and figure.

Some parrots are not pests. All parrots are pets. Thus, no pets are pests.

OAE-3, invalid

Howard – Chapter 06 #94

Subject area: Venn diagrams and categorical syllogisms

95. Put the following categorical syllogism into standard form and identify its mood and figure.

All criminal actions are wicked deeds. All prosecutions for murder are criminal actions. Thus, all

prosecutions for murder are wicked deeds.

AAA-1, valid

Howard – Chapter 06 #95

Subject area: Venn diagrams and categorical syllogisms

96. Put the following categorical syllogism into standard form and identify its mood and figure.

No writers of lewd and sensational articles are honest and decent citizens, but some journalists are

not writers of lewd and sensational articles; consequently some journalists are honest and decent

citizens.

EOI-1, invalid

Howard – Chapter 06 #96

Subject area: Venn diagrams and categorical syllogisms

97. Put the following categorical syllogism into standard form and identify its mood and figure.

Some spaniels are not good hunters, though all spaniels are gentle dogs. Thus, no gentle dogs are good

hunters.

OAE-3, invalid

Howard – Chapter 06 #97

Subject area: Venn diagrams and categorical syllogisms

98. Put the following categorical syllogism into standard form and identify its mood and figure.

All professional wrestlers are good actors, because some good actors are not powerful athletes and all

professional wrestlers are powerful athletes.

OAA-2, invalid

Howard – Chapter 06 #98

Subject area: Venn diagrams and categorical syllogisms

99. Put the following categorical syllogism into standard form and identify its mood and figure.

All storm troopers are metalheads, so some storm troopers are not ballet afficionados, since some

ballet afficionados are metalheads.

IAO-2, invalid

Howard – Chapter 06 #99

Subject area: Venn diagrams and categorical syllogisms

100. Put the following categorical syllogism into standard form and identify its mood and figure.

No reticulocytes are leukocytes, but all phagocytic cells are reticulocytes. Whence it follows that no

phagocytic cells are leukocytes.

EAE-1, valid

Howard – Chapter 06 #100

Subject area: Venn diagrams and categorical syllogisms

101. Put the following categorical syllogism into standard form and identify its mood and figure.

Some calyculated planets are high-orbiting satellites. But some zoantharians are calyculated planets,

since some high-orbiting satellites are zoantharians.

III-4, invalid

Howard – Chapter 06 #101

Subject area: Venn diagrams and categorical syllogisms

102. Put the following categorical syllogism into standard form and identify its mood and figure.

No Shoshoneans are Tylezian mud-dobbers, but all Shoshoneans are quixotic members of the

Uto-Aztecan phylum. So, some Tylezian mud-dobbers are quixotic members of the Uto-Aztecan

phylum.

AEI-3, invalid

Howard – Chapter 06 #102

Subject area: Venn diagrams and categorical syllogisms

103. Put the following categorical syllogism into standard form and identify its mood and figure.

Some Necromonicons are Talmudic doctrines, given that all Linneaen manuscripts are

Necromonicons and some Talmudic doctrines are Linneaen manuscripts.

IAI-4, valid

Howard – Chapter 06 #103

Subject area: Venn diagrams and categorical syllogisms

104. Put the following categorical syllogism into standard form and identify its mood and figure.

Since no hobbits are grand wizards and some grand wizards are members of the Circle of Seven, it

follows that some members of the Circle of Seven are not hobbits.

EIO-4, valid

Howard – Chapter 06 #104

Subject area: Venn diagrams and categorical syllogisms

105. Identify the missing step in the following argument (remember the principles of charity and fairness!

). Then put the argument into standard form. To cut down on writing, use capital letters to abbreviate

English terms.

Because all whales are mammals, at least some aquatic animals are mammals.

All W are M.

Some A are W.

So, some A are M.

Valid

Howard – Chapter 06 #105

Subject area: Enthymemes

106. Identify the missing step in the following argument (remember the principles of charity and fairness!

). Then put the argument into standard form. To cut down on writing, use capital letters to abbreviate

English terms.

No fallacies are valid arguments, since no valid arguments are mistakes in reasoning.

No V are M.

All F are M.

So, no F are V.

Valid

Howard – Chapter 06 #106

Subject area: Enthymemes

107. Identify the missing step in the following argument (remember the principles of charity and fairness!

). Then put the argument into standard form. To cut down on writing, use capital letters to abbreviate

English terms.

Since all chickens are egg-layers, it follows that no chickens are mammals.

All C are E.

No E are M.

So, no C are M.

Valid

Howard – Chapter 06 #107

Subject area: Enthymemes

108. Identify the missing step in the following argument (remember the principles of charity and fairness!

). Then put the argument into standard form. To cut down on writing, use capital letters to abbreviate

English terms.

All psychics are frauds, because all psychics are people who make false claims about their

abilities.

All C are F.

All P are C.

So, all P are F.

Valid

Howard – Chapter 06 #108

Subject area: Enthymemes

109. Identify the missing step in the following argument (remember the principles of charity and fairness!

). Then put the argument into standard form. To cut down on writing, use capital letters to abbreviate

English terms.

It must be that some tabloid reporters are gossipmongers because all overzealous journalists are

tabloid reporters.

Answers will vary

Howard – Chapter 06 #109

Subject area: Enthymemes

110. Identify the missing step in the following argument (remember the principles of charity and fairness!

). Then put the argument into standard form. To cut down on writing, use capital letters to abbreviate

English terms.

Some arguments are sound arguments because some arguments are valid arguments and all valid

arguments are sound arguments.

Answers will vary

Howard – Chapter 06 #110

Subject area: Enthymemes

6 Summary

Category # of Questions

Howard – Chapter 06 110

Subject area: 6.1 Standard Form, Mood, and Figure 16

Subject area: 6.2 Venn Diagrams and Categorical Statements 6

Subject area: 6.3 Venn Diagrams and Categorical Syllogisms 4

Subject area: 6.4 The Modern Square of Opposition 6

Subject area: 6.5 Enthymemes 5

Subject area: 6.6 Sorites and Removing Term-Complements 9

Subject area: 6.7 Rules for Evaluating Syllogisms 11

Subject area: Enthymemes 6

Subject area: Putting syllogisms into standard form 15

Subject area: Removing term-complements 5

Subject area: Rules for evaluating syllogisms 5

Subject area: The Modern Square of Opposition 1

Subject area: Venn diagrams and categorical syllogisms 20

7

Student: ___________________________________________________________________________

1. In (A ⋁ B) → [B • (C ⋁ ~D)], what is the main logical operator?

A. the first occurrence of ⋁

B. •

C. →

D. the second occurrence of ⋁

2. Which of the following is an atomic statement?

A. Sailing is an enjoyable sport.

B. Sewing and cross-stitch require good eyesight.

C. The Cincinnati Reds did not win their last game.

D. Either Sue or Karen will get the high score.

3. Where “F” stands for “Fred likes ice cream” and “L” stands for “Lou likes ice cream,” the

statement “Neither Fred nor Lou likes ice cream” is best symbolized by

A. ~F ⋁ ~L.

B. ~F • ~L.

C. ~F → ~L.

D. ~(F • L).

4. Where “F” stands for “Fred likes ice cream” and “L” stands for “Lou likes ice cream,” the

statement “Either Fred or Lou doesn’t like ice cream” is best symbolized by

A. ~F ⋁ ~L.

B. ~F • ~L.

C. ~F → ~L.

D. ~(F • L).

5. Where “F” stands for “Fred likes ice cream” and “L” stands for “Lou likes ice cream,” the statement “Fred

doesn’t like ice cream only if Lou doesn’t like ice cream” is best symbolized by

A. ~F ⋁ ~L.

B. ~F • ~L.

C. ~F → ~L.

D. ~(F • L).

6. The “⋁” sign is used to symbolize

A. “Either . . . or . . . but not both.”

B. “If . . . then . . .”

C. “Both . . . and . . .”

D. “Either . . . or . . . or both.”

7. In A → B,

A. A provides a necessary condition for B.

B. B provides a sufficient condition for A.

C. A provides a sufficient condition for B.

D. A provides both a necessary and sufficient condition for B.

8. Which of the following is not a condition for a symbolic expression to be a well-formed formula (WFF)?

A. If p is a WFF, then so is ~(p).

B. If p and q are WFFs, then so is (p • q).

C. If p and q are WFFs, then so is (p ⋁ q).

D. If p and q are WFFs, then so is (p → q).

9. Which of the following is not a well-formed formula (WFF)?

A. (~A → B ⋁ C)

B. ~A → (B ⋁ C)

C. ~(A → B) ⋁ C

D. (~A → B) ⋁ C

10. A compound statement is truth-functional if

A. more than one atomic statement is a component.

B. its truth value is a function of the content of its component atomic statement(s).

C. in most contexts it functions as a true statement.

D. its truth value is a function of the truth value of its component atomic statements.

11. On which assignment of truth values does the sentence A → ~B turn out to be false?

A. A is true, and B is true.

B. A is true, and B is false.

C. A is false, and B is true.

D. A is false, and B is false.

12. Under which assignment of truth values does the sentence A ↔ (B • ~C) turn out to be true?

A. A is true, B is false, and C is false.

B. A is false, B is true, and C is false.

C. A is false, B is false, and C is false.

D. A is true, B is false, and C is true.

13. Under which assignment of truth values does the sentence (A ↔ ~B) • ~C turn out to be true?

A. A is true, B is false, and C is false.

B. A is true, B is true, and C is false.

C. A is false, B is false, and C is false.

D. A is true, B is false, and C is true.

14. The truth table for a symbolized argument containing four statement letters will have

A. 4 rows.

B. 8 rows.

C. 12 rows.

D. 16 rows.

15. Using a truth table, we can tell that an argument is valid if

A. there is at least one row where the premises and conclusion are all true.

B. there is no row where the premises are true and the conclusion is false.

C. there is no row where the conclusion is false.

D. there is at least one row where the premises are all true and the conclusion is false.

16. A compound statement is a tautology if

A. it is false regardless of the truth values assigned to the atomic sentences that compose it.

B. its truth value is a function of the truth values of its component atomic sentences.

C. it is true regardless of the truth values assigned to its component atomic sentences.

D. its truth value is a function of the placement of its parentheses.

17. A compound statement is a contradiction if

A. it is false regardless of the truth values assigned to the atomic sentences that compose it.

B. its truth value is a function of the truth values of its component atomic sentences.

C. it is true regardless of the truth values assigned to its component atomic sentences.

D. its truth value is a function of the placement of its parentheses.

18. When two statements are logically equivalent, the columns in the truth table under their main logical

operators

A. show neither statement is contingent.

B. are exactly alike.

C. are exactly opposite.

D. show both statements are tautologies.

19. An atomic statement is a statement that has no other statement as a component.

True False

20. A compound statement is one that has at least one atomic statement as a component.

True False

21. “Chocolate is not nutritious” is an atomic statement.

True False

22. “All roses are red flowers” is a compound statement.

True False

23. In A • B, the statement constants are called disjuncts.

True False

24. The symbol for disjunction represents inclusive “or.”

True False

25. In A → B, the consequent is B.

True False

26. The statement ~A ⋁ B is a negation.

True False

27. A sufficient condition is a condition that, if lacking, guarantees that a statement is false (or that a

phenomenon will not occur).

True False

28. A necessary condition is a condition that guarantees that a statement is true (or that a phenomenon will

occur).

True False

29. The consequent of a true conditional statement provides a necessary condition for the truth of the

antecedent.

True False

30. The English phrase “if and only if” is symbolized with the “↔”.

True False

31. A statement variable is a lower case letter that serves as a placeholder for any statement.

True False

32. (A → B ⋁ C) is a well-formed formula.

True False

33. (A → (B ⋁ C) ⋁ D) is a well-formed formula.

True False

34. In A ⋁ (B • C), the main logical operator is the “⋁”.

True False

35. In (A ⋁ (B) • (D ⋁ C), the main logical operator is the “⋁”.

True False

36. A compound statement is truth functional if its truth value is completely determined by the truth value of

the atomic statements that compose it.

True False

37. A conjunction is true if either one of its conjuncts is true; otherwise, it is false.

True False

38. A disjunction is false if both its disjuncts are false; otherwise it is true.

True False

39. A material conditional is false if its antecedent is true and its consequent is false; otherwise, it is true.

True False

40. A material biconditional is true when its two constituent statements have different truth values;

otherwise, it is true.

True False

41. An argument is valid when it is not possible for its conclusion to be false when all of its premises are

true.

True False

42. The truth table for an argument that has three component atomic statements will have six rows.

True False

43. The abbreviated truth table method can be used to prove that an argument is valid.

True False

44. If there is any assignment of truth values in which the premises are all true and the conclusion is false,

then the argument is invalid.

True False

45. A tautology is a statement that is necessarily false—that is, it is false regardless of the truth values

assigned to the atomic statements that compose it.

True False

46. A statement that is false regardless of the truth values assigned to the atomic statements that compose it is

a contradiction.

True False

47. Any argument with logically inconsistent premises will be valid yet unsound.

True False

48. A statement that is true in at least one row of the truth table and false in at least one row is contingent.

True False

49. Two statements are logically equivalent when each validly implies the other.

True False

50. Two statements are logically equivalent when the biconditional connecting them is a tautology.

True False

51. Making the assumption that A is true, B is true, C is false, and D is false, determine the truth value (true

or false) of this compound statement: A • C

True False

52. Making the assumption that A is true, B is true, C is false, and D is false, determine the truth value (true

or false) of this compound statement: B • ~C

True False

53. Making the assumption that A is true, B is true, C is false, and D is false, determine the truth value (true

or false) of this compound statement: D ⋁ B

True False

54. Making the assumption that A is true, B is true, C is false, and D is false, determine the truth value (true

or false) of this compound statement: C → ~(C • B)

True False

55. Making the assumption that A is true, B is true, C is false, and D is false, determine the truth value (true

or false) of this compound statement: A ↔ (C ⋁ D)

True False

56. Making the assumption that A is true, B is true, C is false, and D is false, determine the truth value (true

or false) of this compound statement: B → ~(A • B)

True False

57. Making the assumption that A is true, B is true, C is false, and D is false, determine the truth value (true

or false) of this compound statement: (A • B) → (A ⋁ ~(C ⋁ B))

True False

58. Making the assumption that A is true, B is true, C is false, and D is false, determine the truth value (true

or false) of this compound statement: ~(A • B) ↔ (A → (C ⋁D))

True False

59. Making the assumption that A is true, B is true, C is false, and D is false, determine the truth value (true

or false) of this compound statement: ~(A → C) • (C ⋁ ~D)

True False

60. Making the assumption that A is true, B is true, C is false, and D is false, determine the truth value (true

or false) of this compound statement: ~(A ⋁ C) ↔ (B • ~(A ⋁ C))

True False

61. Symbols list

You may use the list below to copy-and-paste the symbols into your answer as needed.

→; ↔; •; ~; ⋁;

Translate the following statement into symbols, using the schemes of abbreviation provided: You can

vote in the Democratic primary election only if you are a registered member of the Democratic Party.

(V: You can vote in the Democratic primary election; R: You are a registered member of the Democratic

Party.)

62. Symbols list

You may use the list below to copy-and-paste the symbols into your answer as needed.

→; ↔; •; ~; ⋁;

Translate the following statement into symbols, using the schemes of abbreviation provided: It’s not the

case that Sally is in love with James, though James is in love with Sally. (S: Sally is in love with James; J:

James is in love with Sally.)

63. Symbols list

You may use the list below to copy-and-paste the symbols into your answer as needed.

→; ↔; •; ~; ⋁;

Translate the following statement into symbols, using the schemes of abbreviation provided: The

presence of H2O on Mars is sufficient for the production of life-forms. (H: H2O is present on Mars; P:

Life-forms are produced on Mars.)

64. Symbols list

You may use the list below to copy-and-paste the symbols into your answer as needed.

→; ↔; •; ~; ⋁;

Translate the following statement into symbols, using the schemes of abbreviation provided: Susan will

be able to go to the graduate school of her choice unless she scores very poorly on her GRE. (C: Susan is

able to go to the graduate school of her choice; P: Susan scores very poorly on her GRE.)

65. Symbols list

You may use the list below to copy-and-paste the symbols into your answer as needed.

→; ↔; •; ~; ⋁;

Translate the following statement into symbols, using the schemes of abbreviation provided: Unless

Sharon passes her final, she will get a C in the class. (P: Sharon passes her final; C: Sharon gets a C in the

class.)

66. Symbols list

You may use the list below to copy-and-paste the symbols into your answer as needed.

→; ↔; •; ~; ⋁;

Translate the following statement into symbols, using the schemes of abbreviation provided: Although

Stephen scored high on the LSAT, he did not get into the law school of his choice. (S: Stephen scored

high on the LSAT; L: Stephen got into the law school of his choice.)

67. Symbols list

You may use the list below to copy-and-paste the symbols into your answer as needed.

→; ↔; •; ~; ⋁;

Translate the following statement into symbols, using the schemes of abbreviation provided: Both Al and

Bob failed to come to the party. (A: Al came to the party; B: Bob came to the party.)

68. Symbols list

You may use the list below to copy-and-paste the symbols into your answer as needed.

→; ↔; •; ~; ⋁;

Translate the following statement into symbols, using the schemes of abbreviation provided: Neither Jean

nor Ron is allergic to shellfish. (J: Jean is allergic to shellfish; R: Ron is allergic to shellfish.)

69. Symbols list

You may use the list below to copy-and-paste the symbols into your answer as needed.

→; ↔; •; ~; ⋁;

Translate the following statement into symbols, using the schemes of abbreviation provided: It is not the

case that neither ostriches nor turkeys can fly. (O: Ostriches can fly; T: Turkeys can fly.)

70. Symbols list

You may use the list below to copy-and-paste the symbols into your answer as needed.

→; ↔; •; ~; ⋁;

Translate the following statement into symbols, using the schemes of abbreviation provided: Jones wins

only if Smith and Brown both lose. (J: Jones wins; S: Smith wins; B: Brown wins.)

71. Symbols list

You may use the list below to copy-and-paste the symbols into your answer as needed.

→; ↔; •; ~; ⋁;

Translate the following statement into symbols, using the schemes of abbreviation provided: Assuming

that Susie is at the horse show, Dee Dee is either at home or at work. (S: Susie is at the horse show; H:

Dee Dee is at home; W: Dee Dee is at work.)

72. Symbols list

You may use the list below to copy-and-paste the symbols into your answer as needed.

→; ↔; •; ~; ⋁;

Translate the following statement into symbols, using the schemes of abbreviation provided: A necessary

condition for Adonis to go camping is that he behave and not bark at other dogs. (C: Adonis goes

camping; B: Adonis behaves; O: Adonis barks at other dogs.)

73. Symbols list

You may use the list below to copy-and-paste the symbols into your answer as needed.

→; ↔; •; ~; ⋁;

Translate the following statement into symbols, using the schemes of abbreviation provided: Nathan’s

attendance in class is both a necessary and sufficient condition for his passing this class. (A: Nathan

attends class; P: Nathan passes class.)

74. Symbols list

You may use the list below to copy-and-paste the symbols into your answer as needed.

→; ↔; •; ~; ⋁;

Translate the following statement into symbols, using the schemes of abbreviation provided: Both

Patricia and Scott are prepared for the test, but Henry is not. (P: Patricia is prepared for the test; S: Scott

is prepared for the test; H: Henry is prepared for the test.)

75. Symbols list

You may use the list below to copy-and-paste the symbols into your answer as needed.

→; ↔; •; ~; ⋁;

Translate the following statement into symbols, using the schemes of abbreviation provided: Either

Abigail and Dieter both go to the dance or neither does. (A: Abigail goes to the dance; D: Dieter goes to

the dance.)

76. Symbols list

You may use the list below to copy-and-paste the symbols into your answer as needed.

→; ↔; •; ~; ⋁;

Translate the following statement into symbols, using the schemes of abbreviation provided: It will either

rain or snow, but not both. (R: It will rain; S: It will snow.)

77. Symbols list

You may use the list below to copy-and-paste the symbols into your answer as needed.

→; ↔; •; ~; ⋁;

Translate the following statement into symbols, using the schemes of abbreviation provided: It will snow

if and only if it is below 32° out and the humidity is greater than 60 percent. (S: It will snow; B: It is

below 32° out; H: The humidity is greater than 60 percent.)

78. Symbols list

You may use the list below to copy-and-paste the symbols into your answer as needed.

→; ↔; •; ~; ⋁;

Translate the following statement into symbols, using the schemes of abbreviation provided: If there’s too

much rain in the early spring and not enough during the summer, the tomato crop will not be very good.

(S: There is too much rain in the spring; I: There is enough rain during the summer; G: The tomato crop is

very good.)

79. Symbols list

You may use the list below to copy-and-paste the symbols into your answer as needed.

→; ↔; •; ~; ⋁;

Translate the following statement into symbols, using the schemes of abbreviation provided: If the

argument has all true premises and a false conclusion, then the argument is not valid. (P: The argument

has all true premises; C: The argument has a true conclusion; V: The argument is valid.)

80. Translate the following statement into symbols, using the schemes of abbreviation provided: Nathan will

go to the Cayman Islands for spring break if and only if he gets an A on his geology mid-term, finishes

his English research paper, and does not lose his job. (C: Nathan will go to the Cayman Islands for spring

break; G: Nathan gets an A on his geology midterm; E: Nathan finishes his English research paper; J:

Nathan loses his job.)

7 Key

1. In (A ⋁ B) → [B • (C ⋁ ~D)], what is the main logical operator?

A. the first occurrence of ⋁

B. •

C. →

D. the second occurrence of ⋁

Howard – Chapter 07 #1

Subject area: 7.1 Symbolizing English Arguments

2. Which of the following is an atomic statement?

A. Sailing is an enjoyable sport.

B. Sewing and cross-stitch require good eyesight.

C. The Cincinnati Reds did not win their last game.

D. Either Sue or Karen will get the high score.

Howard – Chapter 07 #2

Subject area: 7.1 Symbolizing English Arguments

3. Where “F” stands for “Fred likes ice cream” and “L” stands for “Lou likes ice cream,” the

statement “Neither Fred nor Lou likes ice cream” is best symbolized by

A. ~F ⋁ ~L.

B. ~F • ~L.

C. ~F → ~L.

D. ~(F • L).

Howard – Chapter 07 #3

Subject area: 7.1 Symbolizing English Arguments

4. Where “F” stands for “Fred likes ice cream” and “L” stands for “Lou likes ice cream,” the

statement “Either Fred or Lou doesn’t like ice cream” is best symbolized by

A. ~F ⋁ ~L.

B. ~F • ~L.

C. ~F → ~L.

D. ~(F • L).

Howard – Chapter 07 #4

Subject area: 7.1 Symbolizing English Arguments

5. Where “F” stands for “Fred likes ice cream” and “L” stands for “Lou likes ice cream,” the

statement “Fred doesn’t like ice cream only if Lou doesn’t like ice cream” is best symbolized by

A. ~F ⋁ ~L.

B. ~F • ~L.

C. ~F → ~L.

D. ~(F • L).

Howard – Chapter 07 #5

Subject area: 7.1 Symbolizing English Arguments

6. The “⋁” sign is used to symbolize

A. “Either . . . or . . . but not both.”

B. “If . . . then . . .”

C. “Both . . . and . . .”

D. “Either . . . or . . . or both.”

Howard – Chapter 07 #6

Subject area: 7.1 Symbolizing English Arguments

7. In A → B,

A. A provides a necessary condition for B.

B. B provides a sufficient condition for A.

C. A provides a sufficient condition for B.

D. A provides both a necessary and sufficient condition for B.

Howard – Chapter 07 #7

Subject area: 7.1 Symbolizing English Arguments

8. Which of the following is not a condition for a symbolic expression to be a well-formed formula

(WFF)?

A. If p is a WFF, then so is ~(p).

B. If p and q are WFFs, then so is (p • q).

C. If p and q are WFFs, then so is (p ⋁ q).

D. If p and q are WFFs, then so is (p → q).

Howard – Chapter 07 #8

Subject area: 7.1 Symbolizing English Arguments

9. Which of the following is not a well-formed formula (WFF)?

A. (~A → B ⋁ C)

B. ~A → (B ⋁ C)

C. ~(A → B) ⋁ C

D. (~A → B) ⋁ C

Howard – Chapter 07 #9

Subject area: 7.1 Symbolizing English Arguments

10. A compound statement is truth-functional if

A. more than one atomic statement is a component.

B. its truth value is a function of the content of its component atomic statement(s).

C. in most contexts it functions as a true statement.

D. its truth value is a function of the truth value of its component atomic statements.

Howard – Chapter 07 #10

Subject area: 7.2 Truth Tables

11. On which assignment of truth values does the sentence A → ~B turn out to be false?

A. A is true, and B is true.

B. A is true, and B is false.

C. A is false, and B is true.

D. A is false, and B is false.

Howard – Chapter 07 #11

Subject area: 7.2 Truth Tables

12. Under which assignment of truth values does the sentence A ↔ (B • ~C) turn out to be true?

A. A is true, B is false, and C is false.

B. A is false, B is true, and C is false.

C. A is false, B is false, and C is false.

D. A is true, B is false, and C is true.

Howard – Chapter 07 #12

Subject area: 7.2 Truth Tables

13. Under which assignment of truth values does the sentence (A ↔ ~B) • ~C turn out to be true?

A. A is true, B is false, and C is false.

B. A is true, B is true, and C is false.

C. A is false, B is false, and C is false.

D. A is true, B is false, and C is true.

Howard – Chapter 07 #13

Subject area: 7.2 Truth Tables

14. The truth table for a symbolized argument containing four statement letters will have

A. 4 rows.

B. 8 rows.

C. 12 rows.

D. 16 rows.

Howard – Chapter 07 #14

Subject area: 7.3 Using Truth Tables to Evaluate Arguments

15. Using a truth table, we can tell that an argument is valid if

A. there is at least one row where the premises and conclusion are all true.

B. there is no row where the premises are true and the conclusion is false.

C. there is no row where the conclusion is false.

D. there is at least one row where the premises are all true and the conclusion is false.

Howard – Chapter 07 #15

Subject area: 7.3 Using Truth Tables to Evaluate Arguments

16. A compound statement is a tautology if

A. it is false regardless of the truth values assigned to the atomic sentences that compose it.

B. its truth value is a function of the truth values of its component atomic sentences.

C. it is true regardless of the truth values assigned to its component atomic sentences.

D. its truth value is a function of the placement of its parentheses.

Howard – Chapter 07 #16

Subject area: 7.5 Tautology, Contradiction, Contingency, and Logical Equivalence

17. A compound statement is a contradiction if

A. it is false regardless of the truth values assigned to the atomic sentences that compose it.

B. its truth value is a function of the truth values of its component atomic sentences.

C. it is true regardless of the truth values assigned to its component atomic sentences.

D. its truth value is a function of the placement of its parentheses.

Howard – Chapter 07 #17

Subject area: 7.5 Tautology, Contradiction, Contingency, and Logical Equivalence

18. When two statements are logically equivalent, the columns in the truth table under their main logical

operators

A. show neither statement is contingent.

B. are exactly alike.

C. are exactly opposite.

D. show both statements are tautologies.

Howard – Chapter 07 #18

Subject area: 7.5 Tautology, Contradiction, Contingency, and Logical Equivalence

19. An atomic statement is a statement that has no other statement as a component.

TRUE

Howard – Chapter 07 #19

Subject area: 7.1 Symbolizing English Arguments

20. A compound statement is one that has at least one atomic statement as a component.

TRUE

Howard – Chapter 07 #20

Subject area: 7.1 Symbolizing English Arguments

21. “Chocolate is not nutritious” is an atomic statement.

FALSE

Howard – Chapter 07 #21

Subject area: 7.1 Symbolizing English Arguments

22. “All roses are red flowers” is a compound statement.

FALSE

Howard – Chapter 07 #22

Subject area: 7.1 Symbolizing English Arguments

23. In A • B, the statement constants are called disjuncts.

FALSE

Howard – Chapter 07 #23

Subject area: 7.1 Symbolizing English Arguments

24. The symbol for disjunction represents inclusive “or.”

TRUE

Howard – Chapter 07 #24

Subject area: 7.1 Symbolizing English Arguments

25. In A → B, the consequent is B.

TRUE

Howard – Chapter 07 #25

Subject area: 7.1 Symbolizing English Arguments

26. The statement ~A ⋁ B is a negation.

FALSE

Howard – Chapter 07 #26

Subject area: 7.1 Symbolizing English Arguments

27. A sufficient condition is a condition that, if lacking, guarantees that a statement is false (or that a

phenomenon will not occur).

FALSE

Howard – Chapter 07 #27

Subject area: 7.1 Symbolizing English Arguments

28. A necessary condition is a condition that guarantees that a statement is true (or that a phenomenon

will occur).

FALSE

Howard – Chapter 07 #28

Subject area: 7.1 Symbolizing English Arguments

29. The consequent of a true conditional statement provides a necessary condition for the truth of the

antecedent.

TRUE

Howard – Chapter 07 #29

Subject area: 7.1 Symbolizing English Arguments

30. The English phrase “if and only if” is symbolized with the “↔”.

TRUE

Howard – Chapter 07 #30

Subject area: 7.1 Symbolizing English Arguments

31. A statement variable is a lower case letter that serves as a placeholder for any statement.

TRUE

Howard – Chapter 07 #31

Subject area: 7.1 Symbolizing English Arguments

32. (A → B ⋁ C) is a well-formed formula.

FALSE

Howard – Chapter 07 #32

Subject area: 7.1 Symbolizing English Arguments

33. (A → (B ⋁ C) ⋁ D) is a well-formed formula.

FALSE

Howard – Chapter 07 #33

Subject area: 7.1 Symbolizing English Arguments

34. In A ⋁ (B • C), the main logical operator is the “⋁”.

TRUE

Howard – Chapter 07 #34

Subject area: 7.1 Symbolizing English Arguments

35. In (A ⋁ (B) • (D ⋁ C), the main logical operator is the “⋁”.

FALSE

Howard – Chapter 07 #35

Subject area: 7.1 Symbolizing English Arguments

36. A compound statement is truth functional if its truth value is completely determined by the truth value

of the atomic statements that compose it.

TRUE

Howard – Chapter 07 #36

Subject area: 7.2 Truth Tables

37. A conjunction is true if either one of its conjuncts is true; otherwise, it is false.

FALSE

Howard – Chapter 07 #37

Subject area: 7.2 Truth Tables

38. A disjunction is false if both its disjuncts are false; otherwise it is true.

TRUE

Howard – Chapter 07 #38

Subject area: 7.2 Truth Tables

39. A material conditional is false if its antecedent is true and its consequent is false; otherwise, it is

true.

TRUE

Howard – Chapter 07 #39

Subject area: 7.2 Truth Tables

40. A material biconditional is true when its two constituent statements have different truth values;

otherwise, it is true.

FALSE

Howard – Chapter 07 #40

Subject area: 7.2 Truth Tables

41. An argument is valid when it is not possible for its conclusion to be false when all of its premises are

true.

TRUE

Howard – Chapter 07 #41

Subject area: 7.3 Using Truth Tables to Evaluate Arguments

42. The truth table for an argument that has three component atomic statements will have six rows.

FALSE

Howard – Chapter 07 #42

Subject area: 7.3 Using Truth Tables to Evaluate Arguments

43. The abbreviated truth table method can be used to prove that an argument is valid.

FALSE

Howard – Chapter 07 #43

Subject area: 7.4 Abbreviated Truth Tables

44. If there is any assignment of truth values in which the premises are all true and the conclusion is false,

then the argument is invalid.

TRUE

Howard – Chapter 07 #44

Subject area: 7.4 Abbreviated Truth Tables

45. A tautology is a statement that is necessarily false—that is, it is false regardless of the truth values

assigned to the atomic statements that compose it.

FALSE

Howard – Chapter 07 #45

Subject area: 7.5 Tautology, Contradiction, Contingency, and Logical Equivalence

46. A statement that is false regardless of the truth values assigned to the atomic statements that compose

it is a contradiction.

TRUE

Howard – Chapter 07 #46

Subject area: 7.5 Tautology, Contradiction, Contingency, and Logical Equivalence

47. Any argument with logically inconsistent premises will be valid yet unsound.

TRUE

Howard – Chapter 07 #47

Subject area: 7.5 Tautology, Contradiction, Contingency, and Logical Equivalence

48. A statement that is true in at least one row of the truth table and false in at least one row is

contingent.

TRUE

Howard – Chapter 07 #48

Subject area: 7.5 Tautology, Contradiction, Contingency, and Logical Equivalence

49. Two statements are logically equivalent when each validly implies the other.

TRUE

Howard – Chapter 07 #49

Subject area: 7.5 Tautology, Contradiction, Contingency, and Logical Equivalence

50. Two statements are logically equivalent when the biconditional connecting them is a tautology.

TRUE

Howard – Chapter 07 #50

Subject area: 7.5 Tautology, Contradiction, Contingency, and Logical Equivalence

51. Making the assumption that A is true, B is true, C is false, and D is false, determine the truth value

(true or false) of this compound statement: A • C

FALSE

Howard – Chapter 07 #51

Subject area: Determining truth values

52. Making the assumption that A is true, B is true, C is false, and D is false, determine the truth value

(true or false) of this compound statement: B • ~C

TRUE

Howard – Chapter 07 #52

Subject area: Determining truth values

53. Making the assumption that A is true, B is true, C is false, and D is false, determine the truth value

(true or false) of this compound statement: D ⋁ B

TRUE

Howard – Chapter 07 #53

Subject area: Determining truth values

54. Making the assumption that A is true, B is true, C is false, and D is false, determine the truth value

(true or false) of this compound statement: C → ~(C • B)

TRUE

Howard – Chapter 07 #54

Subject area: Determining truth values

55. Making the assumption that A is true, B is true, C is false, and D is false, determine the truth value

(true or false) of this compound statement: A ↔ (C ⋁ D)

FALSE

Howard – Chapter 07 #55

Subject area: Determining truth values

56. Making the assumption that A is true, B is true, C is false, and D is false, determine the truth value

(true or false) of this compound statement: B → ~(A • B)

FALSE

Howard – Chapter 07 #56

Subject area: Determining truth values

57. Making the assumption that A is true, B is true, C is false, and D is false, determine the truth value

(true or false) of this compound statement: (A • B) → (A ⋁ ~(C ⋁ B))

TRUE

Howard – Chapter 07 #57

Subject area: Determining truth values

58. Making the assumption that A is true, B is true, C is false, and D is false, determine the truth value

(true or false) of this compound statement: ~(A • B) ↔ (A → (C ⋁D))

TRUE

Howard – Chapter 07 #58

Subject area: Determining truth values

59. Making the assumption that A is true, B is true, C is false, and D is false, determine the truth value

(true or false) of this compound statement: ~(A → C) • (C ⋁ ~D)

TRUE

Howard – Chapter 07 #59

Subject area: Determining truth values

60. Making the assumption that A is true, B is true, C is false, and D is false, determine the truth value

(true or false) of this compound statement: ~(A ⋁ C) ↔ (B • ~(A ⋁ C))

TRUE

Howard – Chapter 07 #60

Subject area: Determining truth values

61. Symbols list

You may use the list below to copy-and-paste the symbols into your answer as needed.

→; ↔; •; ~; ⋁;

Translate the following statement into symbols, using the schemes of abbreviation provided: You

can vote in the Democratic primary election only if you are a registered member of the Democratic

Party. (V: You can vote in the Democratic primary election; R: You are a registered member of the

Democratic Party.)

V → R

Howard – Chapter 07 #61

Subject area: Symbolizing

62. Symbols list

You may use the list below to copy-and-paste the symbols into your answer as needed.

→; ↔; •; ~; ⋁;

Translate the following statement into symbols, using the schemes of abbreviation provided: It’s not

the case that Sally is in love with James, though James is in love with Sally. (S: Sally is in love with

James; J: James is in love with Sally.)

~S • J

Howard – Chapter 07 #62

Subject area: Symbolizing

63. Symbols list

You may use the list below to copy-and-paste the symbols into your answer as needed.

→; ↔; •; ~; ⋁;

Translate the following statement into symbols, using the schemes of abbreviation provided: The

presence of H2O on Mars is sufficient for the production of life-forms. (H: H2O is present on Mars; P:

Life-forms are produced on Mars.)

H → P

Howard – Chapter 07 #63

Subject area: Symbolizing

64. Symbols list

You may use the list below to copy-and-paste the symbols into your answer as needed.

→; ↔; •; ~; ⋁;

Translate the following statement into symbols, using the schemes of abbreviation provided: Susan

will be able to go to the graduate school of her choice unless she scores very poorly on her GRE. (C:

Susan is able to go to the graduate school of her choice; P: Susan scores very poorly on her GRE.)

C ⋁ P

Howard – Chapter 07 #64

Subject area: Symbolizing

65. Symbols list

You may use the list below to copy-and-paste the symbols into your answer as needed.

→; ↔; •; ~; ⋁;

Translate the following statement into symbols, using the schemes of abbreviation provided: Unless

Sharon passes her final, she will get a C in the class. (P: Sharon passes her final; C: Sharon gets a C in

the class.)

C ⋁ P

Howard – Chapter 07 #65

Subject area: Symbolizing

66. Symbols list

You may use the list below to copy-and-paste the symbols into your answer as needed.

→; ↔; •; ~; ⋁;

Translate the following statement into symbols, using the schemes of abbreviation provided: Although

Stephen scored high on the LSAT, he did not get into the law school of his choice. (S: Stephen scored

high on the LSAT; L: Stephen got into the law school of his choice.)

S • ~L

Howard – Chapter 07 #66

Subject area: Symbolizing

67. Symbols list

You may use the list below to copy-and-paste the symbols into your answer as needed.

→; ↔; •; ~; ⋁;

Translate the following statement into symbols, using the schemes of abbreviation provided: Both Al

and Bob failed to come to the party. (A: Al came to the party; B: Bob came to the party.)

~A • ~B

Howard – Chapter 07 #67

Subject area: Symbolizing

68. Symbols list

You may use the list below to copy-and-paste the symbols into your answer as needed.

→; ↔; •; ~; ⋁;

Translate the following statement into symbols, using the schemes of abbreviation provided: Neither

Jean nor Ron is allergic to shellfish. (J: Jean is allergic to shellfish; R: Ron is allergic to shellfish.)

~J • ~R or ~(J ⋁R)

Howard – Chapter 07 #68

Subject area: Symbolizing

69. Symbols list

You may use the list below to copy-and-paste the symbols into your answer as needed.

→; ↔; •; ~; ⋁;

Translate the following statement into symbols, using the schemes of abbreviation provided: It is not

the case that neither ostriches nor turkeys can fly. (O: Ostriches can fly; T: Turkeys can fly.)

~(~O • ~T)

Howard – Chapter 07 #69

Subject area: Symbolizing

70. Symbols list

You may use the list below to copy-and-paste the symbols into your answer as needed.

→; ↔; •; ~; ⋁;

Translate the following statement into symbols, using the schemes of abbreviation provided: Jones

wins only if Smith and Brown both lose. (J: Jones wins; S: Smith wins; B: Brown wins.)

J → (~S • ~B)

Howard – Chapter 07 #70

Subject area: Symbolizing

71. Symbols list

You may use the list below to copy-and-paste the symbols into your answer as needed.

→; ↔; •; ~; ⋁;

Translate the following statement into symbols, using the schemes of abbreviation provided:

Assuming that Susie is at the horse show, Dee Dee is either at home or at work. (S: Susie is at the

horse show; H: Dee Dee is at home; W: Dee Dee is at work.)

S → (H ⋁W)

Howard – Chapter 07 #71

Subject area: Symbolizing

72. Symbols list

You may use the list below to copy-and-paste the symbols into your answer as needed.

→; ↔; •; ~; ⋁;

Translate the following statement into symbols, using the schemes of abbreviation provided: A

necessary condition for Adonis to go camping is that he behave and not bark at other dogs. (C: Adonis

goes camping; B: Adonis behaves; O: Adonis barks at other dogs.)

C → (B • ~O)

Howard – Chapter 07 #72

Subject area: Symbolizing

73. Symbols list

You may use the list below to copy-and-paste the symbols into your answer as needed.

→; ↔; •; ~; ⋁;

Translate the following statement into symbols, using the schemes of abbreviation provided: Nathan’s

attendance in class is both a necessary and sufficient condition for his passing this class. (A: Nathan

attends class; P: Nathan passes class.)

A ↔ P

Howard – Chapter 07 #73

Subject area: Symbolizing

74. Symbols list

You may use the list below to copy-and-paste the symbols into your answer as needed.

→; ↔; •; ~; ⋁;

Translate the following statement into symbols, using the schemes of abbreviation provided: Both

Patricia and Scott are prepared for the test, but Henry is not. (P: Patricia is prepared for the test; S:

Scott is prepared for the test; H: Henry is prepared for the test.)

(P • S) • ~H

Howard – Chapter 07 #74

Subject area: Symbolizing

75. Symbols list

You may use the list below to copy-and-paste the symbols into your answer as needed.

→; ↔; •; ~; ⋁;

Translate the following statement into symbols, using the schemes of abbreviation provided: Either

Abigail and Dieter both go to the dance or neither does. (A: Abigail goes to the dance; D: Dieter goes

to the dance.)

(A • D) ⋁ ~(A ⋁ D)

Howard – Chapter 07 #75

Subject area: Symbolizing

76. Symbols list

You may use the list below to copy-and-paste the symbols into your answer as needed.

→; ↔; •; ~; ⋁;

Translate the following statement into symbols, using the schemes of abbreviation provided: It will

either rain or snow, but not both. (R: It will rain; S: It will snow.)

(R ⋁ S) • ~(R • S)

Howard – Chapter 07 #76

Subject area: Symbolizing

77. Symbols list

You may use the list below to copy-and-paste the symbols into your answer as needed.

→; ↔; •; ~; ⋁;

Translate the following statement into symbols, using the schemes of abbreviation provided: It will

snow if and only if it is below 32° out and the humidity is greater than 60 percent. (S: It will snow; B:

It is below 32° out; H: The humidity is greater than 60 percent.)

S ↔ (B • H)

Howard – Chapter 07 #77

Subject area: Symbolizing

78. Symbols list

You may use the list below to copy-and-paste the symbols into your answer as needed.

→; ↔; •; ~; ⋁;

Translate the following statement into symbols, using the schemes of abbreviation provided: If there’s

too much rain in the early spring and not enough during the summer, the tomato crop will not be very

good. (S: There is too much rain in the spring; I: There is enough rain during the summer; G: The

tomato crop is very good.)

(S • ~I) → ~G

Howard – Chapter 07 #78

Subject area: Symbolizing

79. Symbols list

You may use the list below to copy-and-paste the symbols into your answer as needed.

→; ↔; •; ~; ⋁;

Translate the following statement into symbols, using the schemes of abbreviation provided: If

the argument has all true premises and a false conclusion, then the argument is not valid. (P: The

argument has all true premises; C: The argument has a true conclusion; V: The argument is valid.)

(P • ~C) → ~V

Howard – Chapter 07 #79

Subject area: Symbolizing

80. Translate the following statement into symbols, using the schemes of abbreviation provided: Nathan

will go to the Cayman Islands for spring break if and only if he gets an A on his geology mid-term,

finishes his English research paper, and does not lose his job. (C: Nathan will go to the Cayman

Islands for spring break; G: Nathan gets an A on his geology midterm; E: Nathan finishes his English

research paper; J: Nathan loses his job.)

Answers will vary

Howard – Chapter 07 #80

Subject area: Symbolizing

7 Summary

Category # of Questions

Howard – Chapter 07 80

Subject area: 7.1 Symbolizing English Arguments 26

Subject area: 7.2 Truth Tables 9

Subject area: 7.3 Using Truth Tables to Evaluate Arguments 4

Subject area: 7.4 Abbreviated Truth Tables 2

Subject area: 7.5 Tautology, Contradiction, Contingency, and Logical Equivalence 9

Subject area: Determining truth values 10

Subject area: Symbolizing 20