Given a non-empty set X, consider the binary operation `**: P(X)xx P(X) ->P(X)` given by `A ** B = AnnB, AA A , B in P(X)` is the power set of X. Show that X is the identity element for this operation and X is the only invertible element in `P(X)` with respect to the operation `**`

Explanation

Given defined :P(X)×P(X)→P(X)

and A∗B=A∩B,A,B∈P(X)

An element X is identify element for a binary operation
if

A∗X=A=X∗A

⟹A∩X=A=X∩A
for A∈P(X)

Weknow that

A∗X=A=X∗A

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