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Let P(A) be the power set of a non-empty...

Let P(A) be the power set of a non-empty set A and a binary operation `@` on P(A) is defined by `X@Y=XcupY` for all `YinP(A).` Prove that, the binary operation `@` is commutative as well as associative on P(A). Find the identity element w.r.t. binary operation `@` on P(A). Also prove that `Phi inP(A)` is the only invertible element in P(A).

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