Question

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

Answer 1

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)