For any sets A and B. show that $P(A∩B)=P(A)∩P(B)˙$

Solution: Solution: let $P(A∩B),P(A),P(B)$are the power sets of the set $A∩B,A,B$ respectively let c is a set where $C∈P(A∩B)$ elements of C$∈(A∩B)$ so, $C∈A$ $C∈B$ so, \displaystyle{C}\in{P}{\left({A}\right)}&{C}\in{P}{\left({B}\right)} $C∈[P(A)∩P(B)]$ = LHS hence proved