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Let X be a non-empty set and * be a binary operation on P(X) (the power set of set X) defined by

Prove that '*' is both commutative and associative on P(X). Find the identity element with respect to '*' on P(X). Also, show that ϕ  P(X) is the only invertible element of P(X).

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 As we studied in earlier class that for sets A, B, C

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