Syllogisms Questions and Answers

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.

Q: Statements: I. Some peace are wars. II. No war is an alliance. Conclusions: I. No peace is alliance. II. At least some peace are alliances.

Correct answer: If either conclusion I or II followsNeither conclusion is established: the peace that are wars are certainly not alliances, but the rest of peace is left open, so we can say neither that no peace is an alliance nor that some are. The two between them, however, cover both possibilities, so either I or II must hold.

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 snakes are idiots. II. Some idiots are people. III. All people are soft. Conclusion - I. Some idiots are not snakes. II. Some people are snakes. III. Some soft are idiots.

Correct answer: Only III followsSome idiots are people and all people are soft, so some idiots are soft - that is, some soft are idiots, conclusion III. Conclusion I asserts idiots who are not snakes, which need not exist, and conclusion II links people to snakes through a particular. Only III follows.

Q: Statements: I. No rose is a lily. II. Some lilies are lotuses. Conclusions: I. No rose is a lotus. II. Some lotuses are not roses

Correct answer: If only conclusion II followsThe lilies that are lotuses are, by the first statement, not roses - so some lotuses are not roses, conclusion II. Conclusion I excludes all lotuses from roses, which does not follow. Only II follows.

Q: Statements: All cups are books. All books are shirts. Conclusions: 1. Some cups are not shirts. 2. Some shirts are cups.

Correct answer: Only (2) conclusion followsAll cups are books and all books are shirts, so all cups are shirts - and therefore some shirts are cups, conclusion 2. Conclusion 1 says the opposite of what follows. Only 2 follows.

Q: Statements: All the actors are girls. All the girls are beautiful. Conclusions: 1. All the actors are beautiful. 2. Some girls are actors.

Correct answer: Both (1) and (2) followAll actors are girls and all girls are beautiful, so all actors are beautiful - conclusion 1. And all actors being girls gives its converse, some girls are actors - conclusion 2. Both follow.

Important Instructions

21.

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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22.

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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23.

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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24.

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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25.

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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26.

Statements:

I. Some peace are wars.

II. No war is an alliance.

Conclusions:

I. No peace is alliance.

II. At least some peace are alliances.

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: C

Correct answer: If either conclusion I or II follows

Neither conclusion is established: the peace that are wars are certainly not alliances, but the rest of peace is left open, so we can say neither that no peace is an alliance nor that some are. The two between them, however, cover both possibilities, so either I or II must hold.

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27.

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 snakes are idiots.
II. Some idiots are people.
III. All people are soft.

Conclusion -

I. Some idiots are not snakes.
II. Some people are snakes.
III. Some soft are idiots.

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

Answer: C

Correct answer: Only III follows

Some idiots are people and all people are soft, so some idiots are soft - that is, some soft are idiots, conclusion III. Conclusion I asserts idiots who are not snakes, which need not exist, and conclusion II links people to snakes through a particular. Only III follows.

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28.

Statements:

I. No rose is a lily.

II. Some lilies are lotuses.

Conclusions:

I. No rose is a lotus.

II. Some lotuses are not roses

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 lilies that are lotuses are, by the first statement, not roses - so some lotuses are not roses, conclusion II. Conclusion I excludes all lotuses from roses, which does not follow. Only II follows.

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29.

Statements: All cups are books. All books are shirts.

Conclusions:

1. Some cups are not shirts.

2. Some shirts are cups.

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 cups are books and all books are shirts, so all cups are shirts - and therefore some shirts are cups, conclusion 2. Conclusion 1 says the opposite of what follows. Only 2 follows.

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30.

Statements: All the actors are girls. All the girls are beautiful.

Conclusions:

1. All the actors are beautiful.

2. Some girls are actors.

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 actors are girls and all girls are beautiful, so all actors are beautiful - conclusion 1. And all actors being girls gives its converse, some girls are actors - conclusion 2. Both follow.

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