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.

To determine the correct relationships, we can convert the given statements into propositional logic and apply the rule of contraposition. According to formal logic, an implication (P → Q) is logically equivalent to its contrapositive (¬Q → ¬P).

Let's denote a correct statement as (C) and an incorrect statement as (I). The given conditions are:

1. X(I) → Z(I). Its contrapositive is: Z(C) → X(C).
2. Y(I) → W(C). Its contrapositive is: W(I) → Y(C).
3. W(C) → X(I). Its contrapositive is: X(C) → W(I).

Evaluating Statement I: "If X is correct, then so is Y." If X is correct (X(C)), then based on the contrapositive of Condition 3, W must be incorrect (W(I)). If W is incorrect (W(I)), then based on the contrapositive of Condition 2, Y must be correct (Y(C)). Therefore, through hypothetical syllogism (the chain rule), X(C) → Y(C). Statement I is logically correct.

Evaluating Statement II: "If Z is correct, then it is not necessary that Y is correct." If Z is correct (Z(C)), the contrapositive of Condition 1 dictates that X must be correct (X(C)). As established above, if X is correct, Y must be correct. Thus, Z(C) → Y(C). This makes Y necessarily correct. Statement II is incorrect because it falsely claims this relationship is not necessary.

Why the other options are incorrect:

• Option B is wrong because Statement II is logically false.
• Option C is wrong because it incorrectly includes Statement II.
• Option D is wrong because it dismisses Statement I, which is demonstrably true.

Takeaway: Converting conditional statements into their contrapositives (P → Q ≡ ¬Q → ¬P) and applying the chain rule of inference is the most systematic way to solve logical reasoning chains in the CSAT.