Mathematics · Sets and Relations

JEE Main 2025 — 28 January, Morning Shift — Question 7

The relation $R=\{(x, y): x, y \in z$ and $x+y$ is even $\}$ is :

Answer: C

$\mathrm{R}=\{(\mathrm{x}, \mathrm{y}), \mathrm{x}+\mathrm{y}$ is even $\mathrm{x}, \mathrm{y} \in \mathrm{z}\}$

reflexive $x+x=2 x$ even

symmetric of $x+y$ is even, then $(y+x)$ is also even

transitive of $x+y$ is even $\& y+z$ is even then $\mathrm{x}+\mathrm{z}$ is also even

So, relation is an equivalence relation.

Answer key and solution verified before publishing.

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