A relation R on set A ={-4,-3,-2,-1,0,1,2,3,4} be defined as R ={( x, y ): x + y is an integer divisible by 2 }. Show that R is an equivalence…

A relation R on set $\displaystyle \mathrm{A}=\{-4,-3,-2,-1,0,1,2,3,4\}$ be defined as $\displaystyle \mathrm{R}=\{(\mathrm{x}, \mathrm{y}): \mathrm{x}+\mathrm{y}$ is an integer divisible by $\displaystyle 2 \}$. Show that R is an equivalence relation. Also, write the equivalence class [$\displaystyle 2$].