Syllogisms Questions and Answers

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.

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. Some dolls can speak. II. Some dolls are bad. Conclusion - I. Bad toys can speak. II. All bad can speak.

Correct answer: Neither I nor II followsThe dolls that can speak and the dolls that are bad need not be the same dolls, so neither conclusion can be drawn. Both go further still, making a claim about bad toys or about all bad things. Neither follows.

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 - I. All bats are lions. II. No cow is lion. III. Some camels are cows. Conclusion - I. Some lions are camels. II. No camel is bat. III. Some bats are cows.

Correct answer: None of theseNo cow is a lion and all bats are lions, so no bat is a cow - which makes conclusion III false. Conclusion I links lions to camels, which the statements do not; and conclusion II claims no camel is a bat, whereas only those camels that are cows are ruled out. None of these follows.

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91.

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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92.

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.

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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93.

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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94.

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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95.

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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96.

I. Some dolls can speak.
II. Some dolls are bad.

Conclusion -

I. Bad toys can speak.
II. All bad can speak.

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

Answer: D

Correct answer: Neither I nor II follows

The dolls that can speak and the dolls that are bad need not be the same dolls, so neither conclusion can be drawn. Both go further still, making a claim about bad toys or about all bad things. Neither follows.

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97.

I. All bats are lions.
II. No cow is lion.
III. Some camels are cows.

Conclusion -

I. Some lions are camels.
II. No camel is bat.
III. Some bats are cows.

A.Only I follows
B.Only II follows
C.Only III follows
D.None of these

Answer: D

Correct answer: None of these

No cow is a lion and all bats are lions, so no bat is a cow - which makes conclusion III false. Conclusion I links lions to camels, which the statements do not; and conclusion II claims no camel is a bat, whereas only those camels that are cows are ruled out. None of these follows.

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