> [!NOTE] **Definition** (Equivalence Relation) > An *equivalence relation* on a set $X$ is a [[Binary Relation|binary relation]] on $X$ that is a [[Reflexive Relation|reflexive]], [[Symmetric Relation|symmetric]] and a [[Transitive Relation|transitive]]. For any $a\in X,$ the [[Equivalence Class|equivalence class]] of $a$ under $\sim,$ denoted $[a],$ is defined as $\{ x \in X \mid x \sim a\}.$ The set of equivalence classes, denoted $X/E,$ is called the *[[Quotient Set|quotient]]* (*quotient set* or *quotient space*) of $X$ by $E.$ > [!Example] Example > [[Congruence Modulo n|Congruence Modulo n]].