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Get Answers to all your Questions
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 ) P ( A ∪ B )
Let, A = {1,3} and B = {3,4}
A B = {1,3,4}
P(A) = { {},{1},{3},{1,3}}
P(B) = { {},{3},{4},{3,4}}
L.H.S = P(A) P(B) = { {
},{1},{3},{1,3},{3,4},{4}}
R.H.S.= P(A B) = { {
},{1},{3},{1,3},{3,4},{4},{1,4},{1,3,4}}
Hence, L.H.S. R.H.S
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