Mathematics · 2025
JEE Main · 23 January 2025, Shift 2 · Q2
Let X= R × R. Define a relation R on X as: ( a_1, b_1) R ( a_2, b_2) ⇔ b_1= b_2. Statement I: R is an equivalence relation. Statement II: For some (…
Let $\displaystyle X=\mathbf{R} \times \mathbf{R}$. Define a relation $\displaystyle R$ on $\displaystyle X$ as :
$$\left(\mathrm{a}_1, \mathrm{~b}_1\right) \mathrm{R}\left(\mathrm{a}_2, \mathrm{~b}_2\right) \Leftrightarrow \mathrm{b}_1=\mathrm{b}_2 .
$$Statement I : R is an equivalence relation.
Statement II : For some $\displaystyle (\mathrm{a}, \mathrm{b}) \in \mathrm{X}$, the set $\displaystyle \mathrm{S}=\{(x, y) \in \mathrm{X}:(x, y) \mathrm{R}(\mathrm{a}, \mathrm{b})\}$ represents a line parallel to $\displaystyle y=x$.
In the light of the above statements, choose the correct answer from the options given below :
Official answer
From NTA’s final answer key for this paper.
(3)
Statement I is true but Statement II is false
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JEE Main 2025 Mathematics question, with the answer from NTA’s final answer key. Where our answers come from.