Two new sets

The power set $P(A)$ is the set of all subsets of $A$. If $A$ has $n$ elements, $P(A)$ has $2^n$.

The product $A$ × $B$ is the set of ordered pairs $(a$, $b)$ with $a \in A$ and $b \in B$. It has $|A|\cdot |B|$ elements.