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Let X be a non-empty set, and P(X) be it...

Let `X` be a non-empty set, and `P(X)` be its power set. If * is an operation defined on the elements of `P(X)` by `A * B=AnnBAAA,BinP(x),` then prove that is a binary operation in `P(x)` which is commutative as well as associative. Find its identity element. If '0' is another binary operation defined an `P(X)` on `AoB = AuuB,` then verify that '0' distributes itself over.

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