Prove or Disprove

Quote:

Originally Posted by faisalnet5

How should i answer following type of question?
"For any set X, let P(X) denote the power set of X. Let A and B be arbitrary sets. Prove or Disprove: P(AuB)=P(A) u P(B)."

Consider two cases.
1) If $C \in \mathcal{P}(A \cup B)$ is it true that $C \in \mathcal{P}(A)$ or $C \in \mathcal{P}(B)$

2) If $D \in (\mathcal{P}(A)\cup\mathcal{P}(B))$ is it true that $D \in \mathcal{P}(A \cup B)$ .

If both of those are true the they are equal.

Otherwise, find a simple counter-example.