There are four statements X, Y, Z and W. Their relations are as follows:

Question

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 (Correct answer)
2. B. II only
3. C. Both I and II
4. D. Neither I nor II

Correct Answer

Option A — I only

Detailed Solution & Explanation

The correct answer is Option A (I only).

Key Points

• Rules: ¬X → ¬Z; ¬Y → W; W → ¬X.
• Statement I (X correct ⇒ Y correct): if Y were incorrect, then W is correct, which forces X incorrect — contradiction. So X correct ⇒ Y correct → true.
• Statement II (Z correct ⇒ Y not necessarily correct): from ¬X → ¬Z, the contrapositive gives Z ⇒ X; and X ⇒ Y (from I). So Z correct actually forces Y correct → Statement II is false.

Additional Information

• Only Statement I holds → Option A.