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UPSC CSE 2026 · PYQ · Logical Reasoning / Conditional Statements · hard

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.

  1. A.I only
  2. B.II only
  3. C.Both I and II✓ Correct
  4. D.Neither I nor II

Explanation

Given: (a) ¬X → ¬Z (equivalently Z → X), (b) ¬Y → W, (c) W → ¬X. Statement I: If X is correct, prove Y is correct. From (c) contrapositive: X → ¬W. From (b) contrapositive: ¬W → Y. So X → ¬W → Y. Hence I is correct. Statement II: If Z is correct, then Y need not be correct. From (a) contrapositive: Z → X. From above X → Y. So Z → X → Y, meaning Y must be correct, contradicting II. Hmm — then II would be incorrect, making answer (a). Let me recheck: 'if X is incorrect, then so is Z' means ¬X → ¬Z, contrapositive Z → X. 'if Y is incorrect, then W is correct' means ¬Y → W, contrapositive ¬W → Y. 'if W is correct, then X is incorrect' means W → ¬X, contrapositive X → ¬W. So X → ¬W → Y. And Z → X → Y. So if Z is correct, Y MUST be correct. Statement II says it is NOT necessary Y is correct — this is false. So only I is correct. Answer is (a) I only.
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