Relation (set theory)

In set theory, a relation $R$ between two sets $A$ and $B$ is a subset of the cartesian product $A\times B$.
For $a\in A$ and $b\in B$, one says that $a$ is related to $b$, denoted as $a \;R \;b$, when $(a,b)\in R$.

Remarks and examples

• When $A=B$, one speaks of a relation on $A$.
• A function is itself a special kind of relation.