Mathematics - Sets and Relations Question with Solution | TestHub

For reflexive $(x,x)\in \mathbb{R},x\in \mathbb{Z}$
$\Rightarrow x+x=2x\to \text{ even }$
For symmetric of $(x,y)\in \mathbb{R}$ then $(y,x)\in \mathbb{R}$ when $x,y\in \mathbb{Z}$
$x+y\to$ even
$\Rightarrow y+x\to \text{ even }$
for transitive if $(x,y)\in \mathbb{R}\Rightarrow x+y\to$ even
$(y,z)\in \mathbb{R}\Rightarrow y+z\to \text{ even }$
$x+2y+z\to$ even
$\Rightarrow x+z$ is even
$\Rightarrow (x,z)\in \mathbb{R}$
$\Rightarrow \mathbb{R}$ is an equivalence relation.