Category:Examples of Equivalence Relations Induced by Preorderings

This category contains examples of 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:

$x \sim_\RR y$ if and only if $x \mathrel \RR y$ and $y \mathrel \RR x$

Then $\sim_\RR$ is known as the equivalence (relation) induced by $\RR$.