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For any sets A and B. show that P(A nnB...

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

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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
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