Let $A$ be a [[Set|set]] and $\mathscr{R}$ an [[Equivalence Relation]]. An **equivalence class** of $a \in A$, often denoted by $[[Set|a]] $\{x \in A: a \mathscr{R} x\}$. [[Reflexive Property|Reflexivity]] guarantees that $a \in[a]$. [[Symmetric Property|Symmetry]] guarantees that if $b \in[a]$, then $a \in[b]$. [[Transitive Property|transitivity]] guarantees that if $a \in[b]$ and $b \in[c]$, then $a \in[c]$.