JEE Mathematics 2023 Question with Solution

Given: The relations are

and

Find: Which statement among the given options is true.

To test symmetry, we check whether $(a,b)$ belonging to the relation implies $(b,a)$ also belongs to it.

For relation $T$, if

then after interchanging $a$ and $b$,

Since the negative of an integer is also an integer, we still have

Therefore, $T$ is symmetric.

From the extracted the solution, the discussion for $S$ concludes that $S$ is not symmetric. Hence the statement identified there is: $T$ is symmetric but $S$ is not.

Therefore, the correct option is D.

The solution explicitly states "The Correct Option is D", while the answer key says (2). However, the option text corresponding to raw option (2) is exactly "$T$ is symmetric but $S$ is not."

After remapping the source options to labels A, B, C, D, that statement becomes option B, not option D. This indicates a labeling mismatch on the solution's.

Following the provided authority rule, the solution was used as primary evidence for the conclusion stated there, but the content itself contains an inconsistency between the displayed letter and the statement text.