Question

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

Answer 1

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

$R$ be the equivalence relation on A.

Set $R=\left\{\right(a,b\left)2divides\right(a-b\left)\right\}$

We have to find equivalnce class $\left[0\right]$

To find equivalence class $\left\{0\right\}$,put $b=0$

$\Rightarrow a-0$ is multiple of $2$ .

$\Rightarrow$ a is multiple of $2$.

Multiples of $2$ in given set are $0,2$ and $4$ .

Hence equivalence class $\left\{0\right\}=\{0,2,4\}$