Question

If relation $R$ on the set $A=\{1,2,3,4,5\}$ is defined as $R=\left\{\right(a,b):a+b\text{is even}\},$ then $\left[2\right],$ the equivalence class of $2$ is

• A. $\{2,3\}$
• B. $\{2,3,4\}$
• C. $\{2,4\}$
• D. $\{1,2,3,4,5\}$

Answer 1

The correct option is C $\{2,4\}$

$R=\left\{\right(a,b):a+b\text{is even}\}$
Equivalence class of $2$ is,
$\left[2\right]=\{b\in A:2Rb\}$
$=\{2+b\text{is even},b\in A\}$
$=\{2,4\}$