# Math Help - proof

1. ## proof

How do you prove the power set of A U the power set of B is a subset of the power set of (A U B)

Let $E\in\left(\wp\left(A\right)\cup\wp\left(B\right)\r ight)$, then clearly $E\subseteq A\vee E\subseteq B\implies E\subseteq A\cup B\implies E\in\wp\left(A\cup B\right)$.