# Math Help - Math proof help

1. ## Math proof help

For any set S, let P(S) denote its power set.

Let A and B be sets. Prove the following claims:

If A is a subset of B, then P(A) is a subset of P(B).

2. Let x$\epsilon$P(A). Then x$\subseteq$A. But A$\subseteq$B. So, by transitivity, x$\subseteq$B. This means that x$\epsilon$P(B). So P(A)$\subseteq$P(B).