\begin{definition}[Definition:Equivalence Relation Induced by Preordering]
Let $\struct {S, \RR}$ be a relational structure such that $\RR$ is a preordering.
Let a relation $\sim_\RR$ be defined on $S$ by:
:$x \sim_\RR y$ {{iff}} $x \mathrel \RR y$ and $y \mathrel \RR x$
Then $\sim_\RR$ is known as the '''equivalence (relation) induced by $\RR$'''.
\end{definition}