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Syllogisms Questions and Answers

Important Instructions
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 -

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.

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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42.

In 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 cats are mad. All sick persons are mad. So, all sick persons are cats.
B. All oranges are white. All figs are oranges. So, all figs are white.
C. No man can crawl. No kite can crawl. So, all men are kites.

Answer: B

Correct answer: B

In B the reasoning runs through: all figs are oranges and all oranges are white, so all figs are white. A commits the same fault as before - cats and sick persons are both mad, which does not make them each other - and C draws a positive conclusion from two negative premises, which is never valid.

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43.

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.

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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44.

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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45.

In the question 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 ugly things are happy. She is ugly. She is happy.
B. All nice things are flat. TVs are flat. TVs are nice things.
C. Potatoes are balls. All balls are fruits. Potatoes are fruits.

Answer: D

Correct answer: A and C

In A the conclusion follows: all ugly things are happy and she is ugly, so she is happy. In C it follows as well: potatoes are balls and all balls are fruits, so potatoes are fruits. B is the familiar fault - nice things are flat and TVs are flat, which does not make TVs nice.

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46.

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.

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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47.

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. Cars are birds.
B. Some birds are ants.
C. Cars are ants.
D. Some Cars are ants.
E. Some Cars are not ants.
F. No car is ant.

Answer: B

Correct answer: ADB

Taking A and D as the premises: cars are birds, and some cars are ants. Those cars are birds and they are ants, so some birds are ants, which is B. The premises must be the first two segments and the conclusion the third, and only this order works.

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48.

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.

A. An eagle lays eggs.
B. All birds lay eggs.
C. Some birds can fly.
D. An eagle cannot fly.
E. An eagle is a bird.
F. An eagle cannot swim.

Answer: B

Correct answer: BEA

Taking B and E as the premises: all birds lay eggs, and an eagle is a bird. It follows that an eagle lays eggs, which is A. The other segments - about flying and swimming - are neither needed nor derivable.

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49.

Statement -

A. Some drugs are illegal. Marble is illegal. Marble is a drug.

B. All wolves are dogs. Some dogs are birds. Some wolves are dogs.

C. All locks are keys. Some keys do not open. Some locks do not open.

Answer: D

Correct answer: None

In A the middle term “illegal” is undistributed: some drugs are illegal and marble is illegal, which does not make marble a drug. In B the third segment follows from the first premise alone, so it is not deduced from both. In C, “some keys do not open” need not touch the locks at all. None of the three qualifies.

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50.

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.

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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