Syllogisms Questions and Answers

Q: In 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. Many writers are not readers. All plumbers are writers. Some plumbers are not readers. B. Boys play cricket. Some girls do not play cricket. Some girls are not boys. C. All Humans live in houses. Some penguins live in houses. Some penguins are Humans.

Correct answer: BIn B the conclusion follows: boys play cricket, and some girls do not - so those girls cannot be boys. In A the first segment says only that many writers are not readers, which need not include the plumbers; and in C the middle term, living in houses, is undistributed.

Q: Statements: All the papers are books. All the bags are books. Some purses are bags. Conclusions: 1. Some papers are bags. 2. Some books are papers. 3. Some books are purses.

Correct answer: Only (2) and (3)All papers are books gives some books are papers, conclusion 2; and some purses being bags, with all bags books, gives some books are purses, conclusion 3. Conclusion 1 links papers to bags, which the statements do not.

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 cables are keyboard. II. All cables are monitors. Conclusion - I. Some monitors are keyboard. II. Some monitors are not keyboard.

Correct answer: Only I followsSome cables are keyboards and all cables are monitors, so those cables are monitors that are keyboards - some monitors are keyboards, conclusion I. Conclusion II asserts monitors that are not keyboards, which need not exist. Only I 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 eyes are ears. II. All ears are noses. Conclusion - I. No eyes are ears. II. Some noses are eyes.

Correct answer: Only II followsAll eyes are ears and all ears are noses, so all eyes are noses - and therefore some noses are eyes, conclusion II. Conclusion I contradicts the first statement outright. Only II follows.

Q: Statements: I. Some entertainers are boring. II. All boring are dusty. Conclusions: I. Some entertainers are dusty. II. All entertainers are dusty.

Correct answer: If only conclusion I followsSome entertainers are boring and all boring are dusty, so those entertainers are dusty - some entertainers are dusty, conclusion I. Conclusion II makes it all entertainers, which the particular first statement cannot support. Only I follows.

Q: Statements: Some keys are staplers. Some staplers are stickers. All the stickers are pens. Conclusions: 1. Some pens are staplers. 2. Some stickers are keys. 3. No sticker is key. 4. Some staplers are keys.

Correct answer: Only (1) and (4) and either (2) or (3)Some staplers are stickers and all stickers are pens, so some pens are staplers - conclusion 1; and some keys being staplers gives some staplers are keys, conclusion 4. Conclusions 2 and 3 concern stickers and keys, which the statements leave open - but between them they cover both possibilities, so either holds.

Q: Statements: Some rats are cats. Some cats are dogs. No dog is cow. Conclusions: 1. No cow is cat. 2. No dog is rat. 3. Some cats are rats.

Correct answer: Only (3)Some rats are cats gives its converse, some cats are rats - conclusion 3. Conclusion 1 needs cows excluded from cats, whereas only dogs are excluded; and conclusion 2 crosses two particulars.

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 lions are bats. II. Some bats are cat. Conclusion - I. All lions are cat. II. No cat are bats.

Correct answer: Neither I nor II followsBoth statements are particular - some lions are bats, some bats are cats - and a chain of “some” carries nothing along it. Conclusion I claims all lions are cats and conclusion II that no cat is a bat, and the second even contradicts what is given. Neither follows.

Q: Statements: All the research scholars are psychologists. Some psychologists are scientists. Conclusions: 1. All the research scholars are scientists. 2. Some research scholars are scientists. 3. Some scientists are psychologists. 4. Some psychologists are research scholars.

Correct answer: Only (3) and (4)Some psychologists are scientists gives its converse, some scientists are psychologists - conclusion 3; and all research scholars being psychologists gives some psychologists are research scholars, conclusion 4. Conclusions 1 and 2 need the psychologists who are scientists to be the research scholars, which is not given.

Q: Statements: All the bottles are boxes. All the boxes are bags. Some bags are trays. Conclusions: 1. Some bottles are trays. 2. Some trays are boxes. 3. All the bottles are bags. 4. Some trays are bags.

Correct answer: Only (3) and (4)All bottles are boxes and all boxes are bags, so all bottles are bags - conclusion 3. Some bags are trays gives its converse, some trays are bags - conclusion 4. Conclusions 1 and 2 need the bags that are trays to be bottles or boxes, which is not given.

Important Instructions

61.

In 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. Many writers are not readers. All plumbers are writers. Some plumbers are not readers.

B. Boys play cricket. Some girls do not play cricket. Some girls are not boys.

C. All Humans live in houses. Some penguins live in houses. Some penguins are Humans.

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

Answer: B

Correct answer: B

In B the conclusion follows: boys play cricket, and some girls do not - so those girls cannot be boys. In A the first segment says only that many writers are not readers, which need not include the plumbers; and in C the middle term, living in houses, is undistributed.

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62.

Statements: All the papers are books. All the bags are books. Some purses are bags.

Conclusions:

1. Some papers are bags.

2. Some books are papers.

3. Some books are purses.

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

Answer: B

Correct answer: Only (2) and (3)

All papers are books gives some books are papers, conclusion 2; and some purses being bags, with all bags books, gives some books are purses, conclusion 3. Conclusion 1 links papers to bags, which the statements do not.

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63.

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 cables are keyboard.
II. All cables are monitors.

Conclusion -

I. Some monitors are keyboard.
II. Some monitors are not keyboard.

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

Some cables are keyboards and all cables are monitors, so those cables are monitors that are keyboards - some monitors are keyboards, conclusion I. Conclusion II asserts monitors that are not keyboards, which need not exist. Only I follows.

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64.

I. All eyes are ears.
II. All ears are noses.

Conclusion -

I. No eyes are ears.
II. Some noses are eyes.

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 eyes are ears and all ears are noses, so all eyes are noses - and therefore some noses are eyes, conclusion II. Conclusion I contradicts the first statement outright. Only II follows.

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65.

Statements:

I. Some entertainers are boring.

II. All boring are dusty.

Conclusions:

I. Some entertainers are dusty.

II. All entertainers are dusty.

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: A

Correct answer: If only conclusion I follows

Some entertainers are boring and all boring are dusty, so those entertainers are dusty - some entertainers are dusty, conclusion I. Conclusion II makes it all entertainers, which the particular first statement cannot support. Only I follows.

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66.

Statements: Some keys are staplers. Some staplers are stickers. All the stickers are pens.

Conclusions:

1. Some pens are staplers.

2. Some stickers are keys.

3. No sticker is key.

4. Some staplers are keys.

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

Answer: D

Correct answer: Only (1) and (4) and either (2) or (3)

Some staplers are stickers and all stickers are pens, so some pens are staplers - conclusion 1; and some keys being staplers gives some staplers are keys, conclusion 4. Conclusions 2 and 3 concern stickers and keys, which the statements leave open - but between them they cover both possibilities, so either holds.

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67.

Statements: Some rats are cats. Some cats are dogs. No dog is cow.

Conclusions:

1. No cow is cat.

2. No dog is rat.

3. Some cats are rats.

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

Answer: D

Correct answer: Only (3)

Some rats are cats gives its converse, some cats are rats - conclusion 3. Conclusion 1 needs cows excluded from cats, whereas only dogs are excluded; and conclusion 2 crosses two particulars.

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68.

I. Some lions are bats.
II. Some bats are cat.

Conclusion -

I. All lions are cat.
II. No cat are bats.

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

Both statements are particular - some lions are bats, some bats are cats - and a chain of “some” carries nothing along it. Conclusion I claims all lions are cats and conclusion II that no cat is a bat, and the second even contradicts what is given. Neither follows.

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69.

Statements: All the research scholars are psychologists. Some psychologists are scientists.

Conclusions:

1. All the research scholars are scientists.

2. Some research scholars are scientists.

3. Some scientists are psychologists.

4. Some psychologists are research scholars.

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

Answer: A

Correct answer: Only (3) and (4)

Some psychologists are scientists gives its converse, some scientists are psychologists - conclusion 3; and all research scholars being psychologists gives some psychologists are research scholars, conclusion 4. Conclusions 1 and 2 need the psychologists who are scientists to be the research scholars, which is not given.

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70.

Statements: All the bottles are boxes. All the boxes are bags. Some bags are trays.

Conclusions:

1. Some bottles are trays.

2. Some trays are boxes.

3. All the bottles are bags.

4. Some trays are bags.

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

Answer: A

Correct answer: Only (3) and (4)

All bottles are boxes and all boxes are bags, so all bottles are bags - conclusion 3. Some bags are trays gives its converse, some trays are bags - conclusion 4. Conclusions 1 and 2 need the bags that are trays to be bottles or boxes, which is not given.

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