Suppose $G$ is a complete graph with two vertices, then the number of all possible sub graphs of $G$ is $5$. Let the set of those sub graphs be denoted by $S=\lbrace \langle \emptyset, \emptyset\rangle, G_1, G_2, G_3, G\rbrace$, where $\langle \emptyset, \emptyset\rangle$ is a null graph. If $P( S)$ is a power set of $S$, then will it be true that
$|P(S)|=2^5$?
I know that it is true for a set in general, but here, i have a little confusion only for the reason that $S$ contains a null graph.