Is it true that for any sets A and B, P (A) ∪ P (B) = P (A ∪ B)? J – InterviewSolution

InterviewSolution

1.

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

Answer»

It is a False statement.

Let, A = {3} and B = {4}

Then,

P(A) = {ϕ , {3}}

And P(B) = {ϕ , {4}}

∴ P(A) ∪ P (B) = {ϕ , {1}, {2}}

Now,

A ∪ B = {1, 2}

And P(A ∪ B) = {ϕ , {1}, {2}, {1, 2}}

Hence,

P(A) ∪ P(B) ≠ P (A ∪ B)

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