Question

Let $R$ be the equivalence relation in the set $A=0,1,2,3,4,5$ given by $R=(a,b):2divides(a-b)$. Write the equivalence class [0].

Answer 1

$A$ = $\{0,1,2,3,4,5\}$

$R$ is an equivalence relation and

$R$ = $\left\{(a,b):2divides(a-b)\right\}$
The elements $x\in A$ satisfying $aRx$ constitute a subset $A_a$ of $A$,
called an equivalence class of $A$ with respect to $R$ determined by $a$.

Thus, $\left[a\right]$ = $\{x:x\in AandaRx\}$

$\therefore$ $\left[0\right]$ = $\{0,2,4\}$