We may think of a relation $R\colon A\mathrel {\rightarrow \kern -9.5pt\mathrlap {|}\kern 6pt}B$ as a function from $A$ to $B$ that is multivalued, assigning to each element $a$ in $A$ a set $R\webleft (a\webright )$ of elements of $B$, thought of as the set of values of $R$ at $a$.
Note that this includes also the possibility of $R$ having no value at all on a given $a\in A$ when $R\webleft (a\webright )=\text{Ø}$.
