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.

The correct option is (a) - I only.

Why this is correct

This is a LOGICAL / VERBAL REASONING question based on conditional logic (If P, then Q). Let's translate the given statements into logical implications:
1. If X is incorrect → Z is incorrect. (Contrapositive: If Z is correct → X is correct)
2. If Y is incorrect → W is correct. (Contrapositive: If W is incorrect → Y is correct)
3. If W is correct → X is incorrect. (Contrapositive: If X is correct → W is incorrect)

Evaluating Statement I: "If X is correct, then so is Y."
From (3), if X is correct, then W must be incorrect.
From (2), if W is incorrect, then Y must be correct.
By combining these, "If X is correct → Y is correct" is a logically valid conclusion. Thus, Statement I is correct.

Evaluating Statement II: "If Z is correct, then it is not necessary that Y is correct."
From (1), if Z is correct, then X must be correct.
As proven in Statement I, if X is correct, then Y must be correct.
Therefore, if Z is correct, Y must be correct. Statement II claims it is "not necessary," which contradicts this logical necessity. Thus, Statement II is incorrect.

Why the other options are incorrect

• Option (b) - II only: This is incorrect because Statement II is logically false; as shown above, the correctness of Z necessitates the correctness of Y.
• Option (c) - Both I and II: This is incorrect because while Statement I is a valid logical deduction, Statement II fails the test of logical necessity derived from the premises.
• Option (d) - Neither I nor II: This is incorrect because Statement I is a direct and valid logical consequence of the chain of implications provided in the question.

Key Concept

The Transitive Property of Implications and the Law of Contrapositives (If P → Q, then ~Q → ~P).