Q13 of 162 Page 1

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