4 Binary relations

A binary relation is one such that there are only two sets contributing to the Cartesian product (of which the relation is a subset). In other words, if $L$ is a binary relation, then $L \subseteq X_1 \times X_2$ , for some sets $X_1$ and $X_2$ .

In the case of a binary relation, as described above, $X_1$ is called the domain, and $X_2$ is called the range. It is also common to use the infix notation for a binary relation. For example, $x L y$ means that $(x,y) \in L \subseteq X_1\times X_2$ .