Answer
$mn$
Work Step by Step
$Proof.$
Let $A$ and $B$ be sets, suppose $A$ has $m$ elements, and suppose $B$ has $n$ elements. We know $A \times B$ is a set of ordered pairs, where the first coordinate of each ordered pair comes from $A$, the second coordinate of each ordered pair comes from $B$, and each element of $A$ is paired with each element of $B$. So each of the $m$ elements in $A$ appears as the first coordinate in $n$ ordered pairs. Hence there are $mn$ distinct ordered pairs in $A \times B._\Box$