Any sets A and B, P(A ∪ B) = P(A) ∪ P(B) Here P is the power set.
Can some show or explain to me how to do this? 
I have failed trying to prove it using laws for set equivalence, it seems my method is wrong.

Suppose $A = \{1\}, B = \{2\}$. Does your statement hold?
i.e. Try finding $\mathscr{P}(A\cup B)$ and $\mathscr{P}(A)\cup\mathscr{P}(B)$
