P(A) is the power set of A. Show that- (i) P(AUB) = P(A) ∩ P(B) is always true, but
(ii) P(AUB) = P(A) U P(B) may not be always true.

Let assume that,

and

and

We know,

Power set of a set A is defined as set of subsets of A.

So,

and

and

and

Now, Consider

and

Now, Consider

and

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