Syllogisms Questions and Answers

Q: In the question below is given a statement followed by two conclusions numbered I and II. Give answer (A) If only I follows (B) If only II follows (C) If either I or II follows (D) If neither I nor II follows (E) If both I and II follow. Statement - I. All dogs are cats. II. All rats are cats. Conclusion - I. No dogs are cat. II. Some cat are rat.

Correct answer: Only II followsAll rats are cats, so its converse holds: some cats are rats - conclusion II. Conclusion I contradicts the first statement, which says all dogs are cats. Only II follows.

Q: Statements: All the harmoniums are instruments. All the instruments are flutes. Conclusions: 1. All the flutes are instruments. 2. All the harmoniums are flutes.

Correct answer: Only (2) conclusion followsAll harmoniums are instruments and all instruments are flutes, so all harmoniums are flutes - conclusion 2. Conclusion 1 reverses a universal: all instruments being flutes does not make all flutes instruments. Only 2 follows.

Q: Statements: Some papers are pens. All the pencils are pens. Conclusions: 1. Some pens are pencils. 2. Some pens are papers.

Correct answer: Both (1) and (2) followAll pencils are pens gives its converse, some pens are pencils - conclusion 1. And some papers being pens gives some pens are papers - conclusion 2. Both follow.

Q: In the question below has a set of three or four statements. Each set of statements is further divided into three segments. Choose the alternative where the third segment in the statement can be logically deduced using both the preceding two, but not just from one of them. Statement - A. All ugly things are happy. She is ugly. She is happy. B. All nice things are flat. TVs are flat. TVs are nice things. C. Potatoes are balls. All balls are fruits. Potatoes are fruits.

Correct answer: A and CIn A the conclusion follows: all ugly things are happy and she is ugly, so she is happy. In C it follows as well: potatoes are balls and all balls are fruits, so potatoes are fruits. B is the familiar fault - nice things are flat and TVs are flat, which does not make TVs nice.

Q: Statements: Some envelops are gums. Some gums are seals. Some seals are adhesives. Conclusions: 1. Some envelopes are seals. 2. Some gums are adhesives. 3. Some adhesives are seals. 4. Some adhesives are gums.

Correct answer: Only (3)Some seals are adhesives gives its converse, some adhesives are seals - conclusion 3. Every other conclusion has to cross two particular statements, and the middle terms in them need not be the same things.

Q: Statements: Some tables are T.V. Some T.V. are radios. Conclusions: 1. Some tables are radios. 2. Some radios are tables. 3. All the radios are T.V. 4. All the T.V. are tables.

Correct answer: None of the four.Both statements are particular - some tables are T.V., some T.V. are radios - and the televisions in the two need not be the same, so nothing links tables to radios. The remaining conclusions turn particulars into universals. None of the four follows.

Q: In the question below is given a statement followed by two conclusions numbered I and II. Give answer (A) If only I follows (B) If only II follows (C) If either I or II follows (D) If neither I nor II follows (E) If both I and II follow. Statement - I. All balls are baskets. II. All baskets are tubs. Conclusion - I. All balls are tubs. II. All tubs are balls.

Correct answer: Only I followsAll balls are baskets and all baskets are tubs, so all balls are tubs - conclusion I. Conclusion II reverses that, and a universal statement does not convert: all tubs need not be balls. Only I follows.

Q: Statements: Some ants are parrots. All the parrots are apples. Conclusions: 1. All the apples are parrots. 2. Some ants are apples.

Correct answer: Only (2) conclusion followsSome ants are parrots and all parrots are apples, so those ants are apples - some ants are apples. Conclusion 1 reverses a universal: all parrots being apples does not make all apples parrots. Only 2 follows.

Q: Statements: No door is dog. All the dogs are cats. Conclusions: 1. No door is cat. 2. No cat is door. 3. Some cats are dogs. 4. All the cats are dogs.

Correct answer: Only (3)All dogs are cats gives its converse, some cats are dogs - conclusion 3. Conclusions 1 and 2 shut doors out of cats altogether, which does not follow: doors are excluded only from dogs. Conclusion 4 reverses a universal.

Q: The question given below has a set of three or four statements. Each set of statements is further divided into three segments. Choose the alternative where the third segment in the statement can be logically deduced using both the preceding two, but not just from one of them. Statement - A. Ravens are white. Ravens are good. All good are white. B. Insects are faster than eagles. All eagles are hawks. Insects are faster than hawks. C. No boy is a saint. Peter is a boy. Peter is a saint.

Correct answer: BTest each set by asking whether the third segment follows from both of the first two together, and from neither alone.A. "Ravens are white" and "Ravens are good" tell you only about ravens. They cannot reach all good things, since there may be good things that are not ravens. Not deducible.B. "All eagles are hawks" puts every eagle inside the class of hawks, so "faster than eagles" carries across to the hawks in question. Neither segment gives it alone - the first says nothing about hawks, the second nothing about speed. Deducible from the two together.C. "No boy is a saint" and "Peter is a boy" give the opposite of the third segment: Peter is not a saint. Not deducible.Only set B works, so the answer is B.

Important Instructions

81.

In the question below is given a statement followed by two conclusions numbered I and II.

Give answer

(A) If only I follows
(B) If only II follows
(C) If either I or II follows
(D) If neither I nor II follows
(E) If both I and II follow.

Statement -

I. All dogs are cats.
II. All rats are cats.

Conclusion -

I. No dogs are cat.
II. Some cat are rat.

A.Only I follows
B.Only II follows
C.Either I or II follows
D.Neither I nor II follows

Answer: B

Correct answer: Only II follows

All rats are cats, so its converse holds: some cats are rats - conclusion II. Conclusion I contradicts the first statement, which says all dogs are cats. Only II follows.

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82.

Statements: All the harmoniums are instruments. All the instruments are flutes.

Conclusions:

1. All the flutes are instruments.

2. All the harmoniums are flutes.

A.Only (1) conclusion follows
B.Only (2) conclusion follows
C.Either (1) or (2) follows
D.Neither (1) nor (2) follows

Answer: B

Correct answer: Only (2) conclusion follows

All harmoniums are instruments and all instruments are flutes, so all harmoniums are flutes - conclusion 2. Conclusion 1 reverses a universal: all instruments being flutes does not make all flutes instruments. Only 2 follows.

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83.

Statements: Some papers are pens. All the pencils are pens.

Conclusions:

1. Some pens are pencils.

2. Some pens are papers.

A.Only (1) conclusion follows
B.Only (2) conclusion follows
C.Either (1) or (2) follows
D.Both (1) and (2) follow

Answer: D

Correct answer: Both (1) and (2) follow

All pencils are pens gives its converse, some pens are pencils - conclusion 1. And some papers being pens gives some pens are papers - conclusion 2. Both follow.

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84.

In the question below has a set of three or four statements. Each set of statements is further divided into three segments. Choose the alternative where the third segment in the statement can be logically deduced using both the preceding two, but not just from one of them.

Statement -

A. All ugly things are happy. She is ugly. She is happy.
B. All nice things are flat. TVs are flat. TVs are nice things.
C. Potatoes are balls. All balls are fruits. Potatoes are fruits.

A.A
B.B
C.A and B
D.A and C

Answer: D

Correct answer: A and C

In A the conclusion follows: all ugly things are happy and she is ugly, so she is happy. In C it follows as well: potatoes are balls and all balls are fruits, so potatoes are fruits. B is the familiar fault - nice things are flat and TVs are flat, which does not make TVs nice.

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85.

Statements: Some envelops are gums. Some gums are seals. Some seals are adhesives.

Conclusions:

1. Some envelopes are seals.

2. Some gums are adhesives.

3. Some adhesives are seals.

4. Some adhesives are gums.

A.Only (3)
B.Only (1)
C.Only (2)
D.Only (4)

Answer: A

Correct answer: Only (3)

Some seals are adhesives gives its converse, some adhesives are seals - conclusion 3. Every other conclusion has to cross two particular statements, and the middle terms in them need not be the same things.

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86.

Statements: Some tables are T.V. Some T.V. are radios.

Conclusions:

1. Some tables are radios.

2. Some radios are tables.

3. All the radios are T.V.

4. All the T.V. are tables.

A.Only (2) and (4)
B.Only (1) and (3)
C.Only (4)
D.None of the four.

Answer: D

Correct answer: None of the four.

Both statements are particular - some tables are T.V., some T.V. are radios - and the televisions in the two need not be the same, so nothing links tables to radios. The remaining conclusions turn particulars into universals. None of the four follows.

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87.

I. All balls are baskets.
II. All baskets are tubs.

Conclusion -

I. All balls are tubs.
II. All tubs are balls.

A.Only I follows
B.Only II follows
C.Either I or II follows
D.Neither I nor II follows

Answer: A

Correct answer: Only I follows

All balls are baskets and all baskets are tubs, so all balls are tubs - conclusion I. Conclusion II reverses that, and a universal statement does not convert: all tubs need not be balls. Only I follows.

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88.

Statements: Some ants are parrots. All the parrots are apples.

Conclusions:

1. All the apples are parrots.

2. Some ants are apples.

A.Only (1) conclusion follows
B.Only (2) conclusion follows
C.Either (1) or (2) follows
D.Neither (1) nor (2) follows

Answer: B

Correct answer: Only (2) conclusion follows

Some ants are parrots and all parrots are apples, so those ants are apples - some ants are apples. Conclusion 1 reverses a universal: all parrots being apples does not make all apples parrots. Only 2 follows.

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89.

Statements: No door is dog. All the dogs are cats.

Conclusions:

1. No door is cat.

2. No cat is door.

3. Some cats are dogs.

4. All the cats are dogs.

A.Only (2) and (4)
B.Only (1) and (3)
C.Only (3) and (4)
D.Only (3)

Answer: D

Correct answer: Only (3)

All dogs are cats gives its converse, some cats are dogs - conclusion 3. Conclusions 1 and 2 shut doors out of cats altogether, which does not follow: doors are excluded only from dogs. Conclusion 4 reverses a universal.

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90.

The question given below has a set of three or four statements. Each set of statements is further divided into three segments. Choose the alternative where the third segment in the statement can be logically deduced using both the preceding two, but not just from one of them.

Statement -

A. Ravens are white. Ravens are good. All good are white.
B. Insects are faster than eagles. All eagles are hawks. Insects are faster than hawks.
C. No boy is a saint. Peter is a boy. Peter is a saint.

Answer: B

Correct answer: B

Test each set by asking whether the third segment follows from both of the first two together, and from neither alone.

A. "Ravens are white" and "Ravens are good" tell you only about ravens. They cannot reach all good things, since there may be good things that are not ravens. Not deducible.

B. "All eagles are hawks" puts every eagle inside the class of hawks, so "faster than eagles" carries across to the hawks in question. Neither segment gives it alone - the first says nothing about hawks, the second nothing about speed. Deducible from the two together.

C. "No boy is a saint" and "Peter is a boy" give the opposite of the third segment: Peter is not a saint. Not deducible.

Only set B works, so the answer is B.

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