Q7. Is it true that for any sets A and B, P ( A ) ∪ P ( B ) = P ( A ∪ B )? Justify your answer.

Answers (1)

No, it is false.

To prove : P ( A ) ∪ P ( B ) \neq P ( A ∪ B )

Let,  A = {1,3}    and    B = {3,4}

        A \cup B = {1,3,4}

P(A) = { {\phi},{1},{3},{1,3}}

P(B) = { {\phi},{3},{4},{3,4}}

L.H.S =       P(A) \cup P(B) = { {\phi},{1},{3},{1,3},{3,4},{4}}

R.H.S.=      P(A \cup B) = {  {\phi},{1},{3},{1,3},{3,4},{4},{1,4},{1,3,4}}

Hence, L.H.S.\neq R.H.S

 

       

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