# Prove the following statement:

$V \subseteq W \Leftrightarrow P(V) \subseteq P(W)$

Where P(X) is the power set of X.

asked Oct 16, 2015 in others

To prove the life side implies the right side,
$\text{ for any } a \in P(V), a \text{ is a subset of }V , a \text { is also a subset of } W,\newline \text{ that is } a \in P(W). \text { so } P(V) \subseteq P(W) \newline \newline \text{ on the other hand if }P(V) \subseteq P(W), \text { then } V\in P(V) \text { implies } V\in P(W). \newline \text{ that is } V \text{ is a subset of } W, \text { hence }} V \subseteq W$