Let R be the equivalence relation on the set Z of the integers given by R

We have,
An equivalence relation, R = {(a, b) : 2 divides a -">−- b}

If $b=0$, then $a-b=a-0=a$

As, 2 divides $a-b$

And, the set of integers which are divided by 2 is $\{0, \pm 2, \pm 4, \pm 6, \ldots\}$

So, the equivalence class $[0]=\{0, \pm 2, \pm 4, \pm 6, \ldots\}$