UPSC Prelims 2026 CSAT, question 36

Topic: Logical reasoning

Q36

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.

Solution.

Answer: (a) I only

The given implications are $(\sim X \Rightarrow \sim Z)$ , $(\sim Y \Rightarrow W)$ , and $(W \Rightarrow \sim X)$ .
Statement I is correct: taking the contrapositives gives $Z \Rightarrow X$ , $X \Rightarrow \sim W$ , and $\sim W \Rightarrow Y$ , so $X \Rightarrow Y$ always holds.
Statement II is incorrect: chaining the implications gives $Z \Rightarrow X \Rightarrow \sim W \Rightarrow Y$ , so whenever $Z$ is correct, $Y$ must necessarily be correct.