# Cartesian Product **The [[set]] of all ordered pairs formed from the elements of two given sets.** > [!NOTE] Cartesian Product > The *Cartesian product* of two sets $A$ and $B$ is the set of all ordered pairs $(a, b)$ where $a$ is in $A$ and $b$ is in $B$. > $A\times B=\{(a,b):a\in A\text{ and } b\in B\}$ > ![[CartesianProduct.svg|500]] The [[cardinality]] of the Cartesian product of two sets is the product of their individual cardinalities. $|A\times B|=|A|\times|B|$