Power Set

The power set of the set $A$ is the set of all subsets of $A$, including the empty set and $A$ itself.

• Notation: $\mathcal{P}(A)$ or $2^A$.
• If $A$ has $n$ elements, then $|\mathcal{P}(A)|=2^n$.
• Example:
  • $A=\{1,2\}$
  • $\mathcal{P}(A)=\{\varnothing ,\{1\},\{2\},\{1,2\}\}$