The relation R=(x,y):x,y Z and x+y is even is:

Question

The relation $R={(x,y):x,y\in Z$ 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.

Solutions · 1