There are four statements X, Y, Z and W. Their relations are as follows : If X is incorrect, then so is Z; if Y is incorrect, then W is correct; if W is correct, then X is incorrect. Which of the following is/are correct? I. If X is correct, then so is Y. II. If Z is correct, then it is not necessary that Y is correct. Select the answer using the code given below.

(a) I only ✓ UPSC's answer
(b) II only
(c) Both I and II
(d) Neither I nor II

Why the answer is (a)

• The given conditions are: (1) ~X → ~Z, (2) ~Y → W, and (3) W → ~X.

• From (2) and (3), we can chain the implications: ~Y → W → ~X. Thus, if Y is incorrect, X must be incorrect (~Y → ~X).

• The contrapositive of ~Y → ~X is X → Y. This means if X is correct, Y must also be correct. Therefore, Statement I is correct.

• Consider Statement II: 'If Z is correct, then it is not necessary that Y is correct.' We know ~X → ~Z, so the contrapositive is Z → X.

• If Z is correct, then X is correct (Z → X). Since X → Y (derived above), it follows that Z → Y.

• Therefore, if Z is correct, Y *must* be correct. Statement II claims it is 'not necessary', which is false. Thus, only Statement I is correct.

Why the other options are wrong

(b) II only: Statement II is incorrect because Z being correct implies X is correct, which in turn necessitates that Y is correct.
(c) Both I and II: Statement II is false because the logical chain Z → X → Y proves that Y must be correct if Z is correct.
(d) Neither I nor II: Statement I is correct because the contrapositive of the chain ~Y → ~X establishes that X being correct implies Y is correct.

Asked in the CSAT Paper II of the UPSC Civil Services Preliminary Examination 2026, held on 24 May 2026. Question and answer key: Union Public Service Commission. Explanation: UPSC Answer Check.