JEE MAIN - Mathematics (2025 - 28th January Morning Shift - No. 4)

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

reflexive and transitive but not symmetric

reflexive and symmetric but not transitive

an equivalence relation

symmetric and transitive but not reflexive

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

reflexive $x+x=2 x$ even

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

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

So, relation is an equivalence relation.