For any sets A and B. show that `P(A nnB) = P(A)nn P(B)dot`

Explanation

let `P(A nn B) , P(A), P(B) `are the power sets of the set `A nn B , A, B` respectively

let c is a set where `C in P(A nnB)`

elements of C`in (A nn B)`

so, `C in A`

`C in B`

so, `C in P(A) & C in P(B)`

`C in [ P(A) nn P(B)]` = LHS

hence proved