Syllogisms Questions and Answers

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 papers are books II. All bags are books III. Some purses are bags Conclusion - I. Some papers are bags II. Some books are papers III. Some books are purses

Correct answer: Both II and III followAll papers are books gives its converse, some books are papers - conclusion II. Some purses are bags and all bags are books, so some purses are books, that is some books are purses - conclusion III. Conclusion I links papers to bags, which the statements do not. Both II and III follow.

Q: Statements: All men are vertebrates. Some mammals are vertebrates. Conclusions: 1. All men are mammals. 2. All mammals are men. 3. Some vertebrates are mammals. 4. All vertebrates are men.

Correct answer: Only (3)Some mammals are vertebrates gives its converse, some vertebrates are mammals. The other three try to link men with mammals, and the only connection is through vertebrates as a predicate in both statements - an undistributed middle, which proves nothing.

Q: Statements: Some cows are crows. Some crows are elephants. Conclusions: 1. Some cows are elephants. 2. All crows are elephants.

Correct answer: Neither (1) nor (2) followsBoth statements are particular - some cows are crows, some crows are elephants - and the crows in the two need not be the same, so nothing links cows to elephants. Conclusion 2 goes further still, making a universal out of a particular. 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. Some buttons are rivers. II. Some rivers are shirts. III. All shirts are people. Conclusion - I. Some people are rivers. II. Some people are buttons. III. Some shirts are buttons.

Correct answer: Only I followsSome rivers are shirts and all shirts are people, so some rivers are people - that is, some people are rivers, conclusion I. Conclusions II and III both need to reach buttons, and the only statement about buttons is particular, so nothing follows. Only I 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 flowers are toys. II. Some toys are idiots. III. Some angels are idiots. Conclusion - I. Some angels are toys. II. Some idiots are flowers. III. Some flowers are angels.

Correct answer: None followsEvery link here runs through a particular statement - some toys are idiots, some angels are idiots - and two particulars can never yield a conclusion. Nothing connects flowers to angels, or angels to toys, or idiots to flowers with any certainty. None follows.

Q: Statements: All the windows are doors. No door is a wall. Conclusions: 1. Some windows are walls. 2. No wall is a door.

Correct answer: Only (2) conclusion followsNo door is a wall, and that converts: no wall is a door - conclusion 2. Conclusion 1 is ruled out altogether, since all windows are doors and no door is a wall. Only 2 follows.

Q: Statements: All the locks are keys. All the keys are bats. Some watches are bats. Conclusions: 1. Some bats are locks. 2. Some watches are keys. 3. All the keys are locks.

Correct answer: Only (1)All locks are keys and all keys are bats, so all locks are bats - and therefore some bats are locks, conclusion 1. Conclusion 2 needs the bats that are watches to be keys, which is not given, and conclusion 3 reverses a universal.

Q: Statements: I. No window is a glass. II. Some glasses are doors. Conclusions: I. No window is a door. II. Some doors are not windows.

Correct answer: If only conclusion II follows.The glasses that are doors are, by the first statement, not windows - so some doors are not windows, conclusion II. Conclusion I excludes all doors from windows, which does not follow. Only II 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 - A. No Z is A. All X is Z. No X is A. B. No Z is A. All X is Z. All X is A. C. Some Z is not A. Some X is Z. Some X is not A.

Correct answer: AIn A the conclusion follows: no Z is A and all X is Z, so no X can be A. B draws the opposite conclusion from the same premises, which contradicts them; and in C both premises are particular or negative-particular, from which nothing follows.

Q: Statements: All the goats are tigers. All the tigers are lions. Conclusions: 1. All the goats are lions. 2. All the lions are goats. 3. Some lions are goats. 4. Some tigers are goats.

Correct answer: Only (1), (3) and (4)All goats are tigers and all tigers are lions, so all goats are lions - conclusion 1 - and its converse, some lions are goats, conclusion 3. All goats being tigers also gives some tigers are goats, conclusion 4. Only conclusion 2 fails, reversing a universal.

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41.

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 papers are books
II. All bags are books
III. Some purses are bags

Conclusion -

I. Some papers are bags
II. Some books are papers
III. Some books are purses

A.Only I follows
B.Only II follows
C.Only III follows
D.Both II and III follow

Answer: D

Correct answer: Both II and III follow

All papers are books gives its converse, some books are papers - conclusion II. Some purses are bags and all bags are books, so some purses are books, that is some books are purses - conclusion III. Conclusion I links papers to bags, which the statements do not. Both II and III follow.

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42.

Statements: All men are vertebrates. Some mammals are vertebrates.

Conclusions:

1. All men are mammals.

2. All mammals are men.

3. Some vertebrates are mammals.

4. All vertebrates are men.

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

Answer: C

Correct answer: Only (3)

Some mammals are vertebrates gives its converse, some vertebrates are mammals. The other three try to link men with mammals, and the only connection is through vertebrates as a predicate in both statements - an undistributed middle, which proves nothing.

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43.

Statements: Some cows are crows. Some crows are elephants.

Conclusions:

1. Some cows are elephants.

2. All crows are elephants.

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

Answer: D

Correct answer: Neither (1) nor (2) follows

Both statements are particular - some cows are crows, some crows are elephants - and the crows in the two need not be the same, so nothing links cows to elephants. Conclusion 2 goes further still, making a universal out of a particular. Neither follows.

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44.

I. Some buttons are rivers.
II. Some rivers are shirts.
III. All shirts are people.

Conclusion -

I. Some people are rivers.
II. Some people are buttons.
III. Some shirts are buttons.

A.Only I follows
B.Only II follows
C.Only III follows
D.Only I and II follows

Answer: A

Correct answer: Only I follows

Some rivers are shirts and all shirts are people, so some rivers are people - that is, some people are rivers, conclusion I. Conclusions II and III both need to reach buttons, and the only statement about buttons is particular, so nothing follows. Only I follows.

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45.

I. All flowers are toys.
II. Some toys are idiots.
III. Some angels are idiots.

Conclusion -

I. Some angels are toys.
II. Some idiots are flowers.
III. Some flowers are angels.

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

Answer: D

Correct answer: None follows

Every link here runs through a particular statement - some toys are idiots, some angels are idiots - and two particulars can never yield a conclusion. Nothing connects flowers to angels, or angels to toys, or idiots to flowers with any certainty. None follows.

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46.

Statements: All the windows are doors. No door is a wall.

Conclusions:

1. Some windows are walls.

2. No wall is a door.

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

No door is a wall, and that converts: no wall is a door - conclusion 2. Conclusion 1 is ruled out altogether, since all windows are doors and no door is a wall. Only 2 follows.

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47.

Statements: All the locks are keys. All the keys are bats. Some watches are bats.

Conclusions:

1. Some bats are locks.

2. Some watches are keys.

3. All the keys are locks.

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

Answer: B

Correct answer: Only (1)

All locks are keys and all keys are bats, so all locks are bats - and therefore some bats are locks, conclusion 1. Conclusion 2 needs the bats that are watches to be keys, which is not given, and conclusion 3 reverses a universal.

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48.

Statements:

I. No window is a glass.

II. Some glasses are doors.

Conclusions:

I. No window is a door.

II. Some doors are not windows.

A.If only conclusion I follows
B.If only conclusion II follows.
C.If either conclusion I or II follows
D.If neither conclusion I nor II follows

Answer: B

Correct answer: If only conclusion II follows.

The glasses that are doors are, by the first statement, not windows - so some doors are not windows, conclusion II. Conclusion I excludes all doors from windows, which does not follow. Only II follows.

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49.

A. No Z is A. All X is Z. No X is A.
B. No Z is A. All X is Z. All X is A.
C. Some Z is not A. Some X is Z. Some X is not A.

Answer: A

Correct answer: A

In A the conclusion follows: no Z is A and all X is Z, so no X can be A. B draws the opposite conclusion from the same premises, which contradicts them; and in C both premises are particular or negative-particular, from which nothing follows.

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50.

Statements: All the goats are tigers. All the tigers are lions.

Conclusions:

1. All the goats are lions.

2. All the lions are goats.

3. Some lions are goats.

4. Some tigers are goats.

A.All the four
B.Only (1), (2) and (3)
C.Only (1), (3) and (4)
D.Only (2), (3) and (4)

Answer: C

Correct answer: Only (1), (3) and (4)

All goats are tigers and all tigers are lions, so all goats are lions - conclusion 1 - and its converse, some lions are goats, conclusion 3. All goats being tigers also gives some tigers are goats, conclusion 4. Only conclusion 2 fails, reversing a universal.

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