QJEEM22Mac038: JEE Main 2022 Mathematics - Class 11 JEEM22Mac038 Solution: Let a set A = A 1 A 2 ..... A k , where A i A j = for i j, 1 j, …

$R = \{ (x,y):y \in {A_i},\,iff\,x \in {A_i}\,1 \le i \ge k\}$

(1) Reflexive

(a, a) $\Rightarrow$ $a \in {A_i}$ iff $a \in {A_i}$

(2) Symmetric

(a, b) $\Rightarrow$ $a \in {A_i}$ iff $b \in {A_i}$

(b, a) $\in$ R as $b \in {A_i}$ iff $a \in {A_i}$

(3) Transitive

(a, b) $\in$ R & (b, c) $\in$ R.

$\Rightarrow$ $a \in {A_i}$ iff $b \in {A_i}$ & $b \in {A_i}$ iff $c \in {A_i}$

$\Rightarrow$ $a \in {A_i}$ iff $c \in {A_i}$

$\Rightarrow$ (a, c) $\in$ R.

$\Rightarrow$ RElation is equivalnece.