Syllogisms Questions and Answers

Q: In this question, three Statements are given, followed by three Conclusions numbered I, II and III. Assuming the statements to be true even if they seem to be at variance with commonly known facts, decide which of the conclusions logically follow(s) from the statements.Statements : Some tables are birds.No bird is pen.All pens are hills.Conclusions : I. Some hills are birds.II. No hill is bird.III. Some tables are pens.

The answer is Either conclusion I or II follows.From 'No bird is pen' and 'All pens are hills', nothing definite follows about birds and hills: some hills may or may not be birds. So neither I ('Some hills are birds') nor II ('No hill is bird') follows by itself.But I and II are a complementary pair about the same two terms: one says some hills are birds, the other that none is. Exactly one of them must be true, so the answer is 'either I or II'. Conclusion III ('Some tables are pens') does not follow, because the tables that are birds cannot be pens, and nothing is said about other tables.

Q: Human beings are one among many creatures that inhabit an imagined world. In this imagined world, some creatures are cruel. If in this imagined world, it is given that the statement “Some human beings are not cruel creatures” is FALSE, then which of the following set of statement(s) can be logically inferred with certainty?(i) All human beings are cruel creatures.(ii) Some human beings are cruel creatures.(iii) Some creatures that are cruel are human beings.(iv) No human beings are cruel creatures.

The statements that follow with certainty are (i), (ii) and (iii).If “Some human beings are not cruel creatures” is false, then there is no human being who is not cruel, so all human beings are cruel creatures: statement (i).Human beings exist in this world (they are among its creatures), so if all of them are cruel, then some human beings are cruel (ii), and equally some cruel creatures are human beings (iii), which is (ii) read the other way round.Statement (iv), “No human beings are cruel creatures”, contradicts (i), so any option containing it is wrong. Options listing only (i), or only (i) and (ii), leave out statements that also follow.

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. All beggars are poor. All lions are poor. So, all lions are beggars. B. All people are boxes. All foxes are people. So, all boxes are foxes. C. All men can run. All women are men. So, all women can run.

Correct answer: CIn C the middle term is properly distributed: all women are men and all men can run, so all women can run - the third segment does follow from the two before it. In A and B the middle term appears as a predicate in both premises, which proves nothing: two classes both contained in a third need not overlap.

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 pens are books. II. All temples are books. III. Some libraries are temples. Conclusion - I. Some libraries are pens. II. Some pens are temples. III. Some libraries are books.

Correct answer: Only III followsSome libraries are temples and all temples are books, so some libraries are books - conclusion III. Conclusions I and II both try to reach pens, and the only statement about pens is a particular one, which cannot carry a conclusion. Only III follows.

Q: Statements: I. Some books are texts. II. Some texts are copies. Conclusions: I. Some books are copies. II. All copies are text.

Correct answer: If neither conclusion I nor II followsBoth statements are particular, and the texts that are books need not be the texts that are copies, so nothing links books to copies. Conclusion II makes a universal out of a particular. Neither follows.

Q: Statements: I. Some leaves are vacations. II. No vacation is holiday. Conclusions: I. Some vacations are leaves. II. No leave is holiday.

Correct answer: If only conclusion I followsSome leaves are vacations gives its converse, some vacations are leaves - conclusion I. Conclusion II excludes every leave from holidays, whereas only the vacations are excluded, and some leaves may be neither. 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. Every photograph is a portrait. II. Every portrait is an artwork. Conclusion I. Every photograph is an artwork. II. Some artworks are portraits.

Correct answer: Both I and II followEvery photograph is a portrait and every portrait an artwork, so every photograph is an artwork - conclusion I. And since every portrait is an artwork, some artworks are portraits - conclusion II, the converse. Both follow.

Q: Statements: I. No point is a brake. II. No catch is a brake. Conclusions: I. Some points are not catches. II. Some brakes are catches.

Correct answer: If neither conclusion I nor II followsBoth statements are negative - no point is a brake, no catch is a brake - and from two negatives nothing follows. Conclusion II even contradicts the second statement. Neither follows.

Q: In the question given below consists of five or six statements followed by options consisting of three statements put together in a specific order. Choose the option which indicates a valid argument containing logically related statements that is, where the third statement is conclusion drawn from preceding two statements. Statement - A. No apple is a door. B. All poles are doors. C. No pole is an apple. D. Some poles are not apples. E. Some apples are poles. F. Some doors are not apples.

Correct answer: ABCTaking A and B as the premises: no apple is a door, and all poles are doors. Anything that is a pole is therefore a door, and no door is an apple - so no pole is an apple, which is C. The other orders offered put a conclusion among the premises or draw more than the premises allow.

Q: Statements: Some cars are jeeps. All the boxes are jeeps. All the pens are cars. Conclusions: 1. Some cars are boxes. 2. No pen is jeep. 3. Some boxes are cars.

Correct answer: None of threeConclusions 1 and 3 link cars with boxes, which are joined only through jeeps as a predicate in both statements - an undistributed middle. Conclusion 2 denies any pen being a jeep, whereas all pens are cars and some cars are jeeps, so nothing of the kind follows. None of the three follows.

Important Instructions

In this question, three Statements are given, followed by three Conclusions numbered I, II and III. Assuming the statements to be true even if they seem to be at variance with commonly known facts, decide which of the conclusions logically follow(s) from the statements.

Statements : Some tables are birds.
No bird is pen.
All pens are hills.

Conclusions : I. Some hills are birds.
II. No hill is bird.
III. Some tables are pens.

A.Only conclusion II follows.
B.All conclusions I, II and III follow.
C.Either conclusion I or II follows.
D.Only conclusion I follows.

Exam Year(s)

CBSE Assistant Secretary - 2024,

Answer: C

The answer is Either conclusion I or II follows.

From 'No bird is pen' and 'All pens are hills', nothing definite follows about birds and hills: some hills may or may not be birds. So neither I ('Some hills are birds') nor II ('No hill is bird') follows by itself.

But I and II are a complementary pair about the same two terms: one says some hills are birds, the other that none is. Exactly one of them must be true, so the answer is 'either I or II'. Conclusion III ('Some tables are pens') does not follow, because the tables that are birds cannot be pens, and nothing is said about other tables.

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Human beings are one among many creatures that inhabit an imagined world. In this imagined world, some creatures are cruel. If in this imagined world, it is given that the statement “Some human beings are not cruel creatures” is FALSE, then which of the following set of statement(s) can be logically inferred with certainty?

(i) All human beings are cruel creatures.
(ii) Some human beings are cruel creatures.
(iii) Some creatures that are cruel are human beings.
(iv) No human beings are cruel creatures.

A.only (i)
B.only (iii) and (iv)
C.only (i) and (ii)
D.(i), (ii) and (iii)

Exam Year(s)

GATE AE - 2023,

Answer: D

The statements that follow with certainty are (i), (ii) and (iii).

If “Some human beings are not cruel creatures” is false, then there is no human being who is not cruel, so all human beings are cruel creatures: statement (i).

Human beings exist in this world (they are among its creatures), so if all of them are cruel, then some human beings are cruel (ii), and equally some cruel creatures are human beings (iii), which is (ii) read the other way round.

Statement (iv), “No human beings are cruel creatures”, contradicts (i), so any option containing it is wrong. Options listing only (i), or only (i) and (ii), leave out statements that also follow.

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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. All beggars are poor. All lions are poor. So, all lions are beggars.
B. All people are boxes. All foxes are people. So, all boxes are foxes.
C. All men can run. All women are men. So, all women can run.

A.A
B.B
C.C
D.None

Answer: C

Correct answer: C

In C the middle term is properly distributed: all women are men and all men can run, so all women can run - the third segment does follow from the two before it. In A and B the middle term appears as a predicate in both premises, which proves nothing: two classes both contained in a third need not overlap.

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I. Some pens are books.
II. All temples are books.
III. Some libraries are temples.

Conclusion -

I. Some libraries are pens.
II. Some pens are temples.
III. Some libraries are books.

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

Answer: C

Correct answer: Only III follows

Some libraries are temples and all temples are books, so some libraries are books - conclusion III. Conclusions I and II both try to reach pens, and the only statement about pens is a particular one, which cannot carry a conclusion. Only III follows.

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Statements:

I. Some books are texts.

II. Some texts are copies.

Conclusions:

I. Some books are copies.

II. All copies are text.

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: D

Correct answer: If neither conclusion I nor II follows

Both statements are particular, and the texts that are books need not be the texts that are copies, so nothing links books to copies. Conclusion II makes a universal out of a particular. Neither follows.

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Statements:

I. Some leaves are vacations.

II. No vacation is holiday.

Conclusions:

I. Some vacations are leaves.

II. No leave is holiday.

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 leaves are vacations gives its converse, some vacations are leaves - conclusion I. Conclusion II excludes every leave from holidays, whereas only the vacations are excluded, and some leaves may be neither. Only I follows.

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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. Every photograph is a portrait.
II. Every portrait is an artwork.

Conclusion

I. Every photograph is an artwork.
II. Some artworks are portraits.

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

Answer: D

Correct answer: Both I and II follow

Every photograph is a portrait and every portrait an artwork, so every photograph is an artwork - conclusion I. And since every portrait is an artwork, some artworks are portraits - conclusion II, the converse. Both follow.

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Statements:

I. No point is a brake.

II. No catch is a brake.

Conclusions:

I. Some points are not catches.

II. Some brakes are catches.

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: D

Correct answer: If neither conclusion I nor II follows

Both statements are negative - no point is a brake, no catch is a brake - and from two negatives nothing follows. Conclusion II even contradicts the second statement. Neither follows.

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In the question given below consists of five or six statements followed by options consisting of three statements put together in a specific order. Choose the option which indicates a valid argument containing logically related statements that is, where the third statement is conclusion drawn from preceding two statements.

Statement -

A. No apple is a door.
B. All poles are doors.
C. No pole is an apple.
D. Some poles are not apples.
E. Some apples are poles.
F. Some doors are not apples.

A.ABC
B.ACB
C.BDA
D.DFA

Answer: A

Correct answer: ABC

Taking A and B as the premises: no apple is a door, and all poles are doors. Anything that is a pole is therefore a door, and no door is an apple - so no pole is an apple, which is C. The other orders offered put a conclusion among the premises or draw more than the premises allow.

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10.

Statements: Some cars are jeeps. All the boxes are jeeps. All the pens are cars.

Conclusions:

1. Some cars are boxes.

2. No pen is jeep.

3. Some boxes are cars.

A.None of three
B.Only (1) and (2)
C.Only (1) and (3)
D.Only (2) and (3)

Answer: A

Correct answer: None of three

Conclusions 1 and 3 link cars with boxes, which are joined only through jeeps as a predicate in both statements - an undistributed middle. Conclusion 2 denies any pen being a jeep, whereas all pens are cars and some cars are jeeps, so nothing of the kind follows. None of the three follows.

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