QUESTION

CSAT

Hard

Reasoning

Prelims 2026

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.

Select an option to attempt

Explanation

Let us represent the statements being correct as $X$ , $Y$ , $Z$ , and $W$ , and the statements being incorrect as $

eg X $,$

eg Y $,$

eg Z $, and$

eg W$.

According to the question, the given relations can be written as logical implications:

If $X$ is incorrect, then $Z$ is incorrect: $

eg X \implies

eg Z $2. If$ Y $is incorrect, then$ W $is correct:$

eg Y \implies W $3. If$ W $is correct, then$ X $is incorrect:$ W \implies

eg X$

By combining these three relations, we can form a continuous chain of implications: $

eg Y \implies W \implies

eg X \implies

eg Z$

In logic, the contrapositive of a statement $A \implies B$ is $

eg B \implies

eg A $, and both always hold the exact same truth value. Taking the contrapositive of our entire chain of implications (reversing the order and negating each term), we get:$ Z \implies X \implies

eg W \implies Y$

Now, let us evaluate the given conclusions based on this contrapositive chain:

Statement I: If $X$ is correct, then so is $Y$ . From our contrapositive chain, we can clearly see that $X \implies Y$ . This means that if $X$ is correct, $Y$ must definitely be correct. Therefore, Statement I is correct.

Statement II: If $Z$ is correct, then it is not necessary that $Y$ is correct. From our contrapositive chain, we can see that $Z \implies Y$ . This means that if $Z$ is correct, it is absolutely necessary that $Y$ is correct. Therefore, Statement II is incorrect.