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• December 14th 2009, 04:00 PM
leinadwerdna
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)
• December 14th 2009, 06:50 PM
Drexel28
Quote:

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