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)
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Originally Posted by leinadwerdna 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 $\displaystyle E\in\left(\wp\left(A\right)\cup\wp\left(B\right)\r ight)$, then clearly $\displaystyle E\subseteq A\vee E\subseteq B\implies E\subseteq A\cup B\implies E\in\wp\left(A\cup B\right)$.
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