Deductive and Inductive Reasoning Questions and Answers

Answer: A

The equivalent of 'All atheists are pessimists' is All non-pessimists are non-atheists.

This is the contrapositive. A universal affirmative 'All S are P' is equivalent to 'All non-P are non-S', obtained by exchanging the terms and negating both.

The statement 'All non-atheists are non-pessimists' is the obverse of the converse, and it does not follow. 'All pessimists are atheists' is the converse, which is not equivalent either. So only the first option is equivalent.

Answer: A

The argument is analogical. It compares two things, a diamond cut into bits and an army divided into small units, and argues that because the first loses value when divided, the second loses strength in the same way. Reasoning from a similarity between two cases is the mark of analogy.

It is not deductive, since the conclusion does not follow necessarily. It is not statistical, as no sample or proportion is used. It is not causal, because no cause-effect link is established between the two cases.

Answer: C

The relation is subcontrary. Two propositions with the same subject and predicate that can both be true but cannot both be false are subcontraries, for example 'Some students are present' and 'Some students are not present'.

Contradictory propositions can neither be both true nor both false. Contrary propositions can both be false but not both true. A subaltern pair is a universal and its particular, where the truth of the universal gives the truth of the particular, and it is not defined by this test.

Answer: C

The valid conclusions are (iii) and (iv). From 'No cats are dogs' we can convert the proposition to 'No dogs are cats', which is (iii). From 'All dogs are mammals' it follows that no dog is a non-mammal, which is (iv).

Conclusion (i), 'No cats are mammals', does not follow, since cats may be mammals while still not being dogs. Conclusion (ii), 'Some cats are mammals', does not follow either, because the premises say nothing about cats being mammals. So only (iii) and (iv) hold.

Answer: B

The region for Indian scientists who are not politicians is s only. Indian scientists lie in the overlap of circle A (Indians) and circle B (scientists), which contains the regions q and s. Region q also lies inside circle C, the politicians, so it must be removed.

That leaves s. The option 'q and s only' wrongly keeps q, which is also a politician. 'p, q and s only' and 's and r only' include regions that fall outside the A and B overlap or inside C.