Power Set

set-theory

Power Set

A power set $P(S)$ is a set of all subsets of a set $S$ and defined as:

$$\mathcal{P}(S)=\{X\mid X\subseteq S\}$$

Example:

$$\mathcal{P}(\{1,2,3\})=\{\varnothing ,\{1\},\{2\},\{3\},\{1,2\},\{1,3\},\{2,3\},\{1,2,3\}\}$$