JEE Mathematics 2023 Question with Solution

Given: $R$ is defined on $\mathbb{N}$ by $a R b$ if $2a + 3b$ is a multiple of $5$.

Find: Which property combination the relation $R$ satisfies.

From the solution:

Reflexivity:

Since $5a$ is a multiple of $5$, $R$ is reflexive.

Symmetry:

The solution states that both are satisfied, so $R$ is symmetric.

Transitivity:

Adding, the solution gives

so $a R c$. Thus, $R$ is transitive.

Therefore, the working in the solution concludes that the relation is reflexive, symmetric, and transitive, which would make it an equivalence relation. However, the solution explicitly declares the correct option as B. Following the solution's authority for the final marked answer, the correct option is B.

The solution contains an internal inconsistency:

• It explicitly says The Correct Option is B.
• But the written explanation says the relation is reflexive, symmetric, and transitive.

Because the solution's explicitly labels B as correct, the extracted answer is recorded as B, while preserving the discrepancy in the solution content.