QJEEM25Mac608: JEE Main 2025 Mathematics - Class 11 JEEM25Mac608 Solution: The relation and is even is:

Question

Verified Solution • 2025–26 Session moderate

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

Accepted Answer

$R=\{(x, y): x, y \in z$ 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.

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