The characteristic relation
\[ \chi _{X}\webleft (-_{1},-_{2}\webright )\colon X\times X\to \{ \mathsf{t},\mathsf{f}\} \]
on $X$ of Chapter 2: Constructions With Sets, Item 3 of Definition 2.4.1.1.1, defined by
\[ \chi _{X}\webleft (x,y\webright ) \mathrel {\smash {\overset {\mathclap {\scriptscriptstyle \text{def}}}=}}\begin{cases} \mathsf{true}& \text{if $x=y$,}\\ \mathsf{false}& \text{if $x\neq y$} \end{cases} \]
for each $x,y\in X$, is another example of a relation.
