(i) | ${\sim} \subseteq X \times X$ is an D178: Equivalence relation on $X$ |

(ii) | \begin{equation} \forall \, x \in X : {\sim}(x) : = \{ y : (x, y) \in {\sim} \} \end{equation} |

**quotient set**of $X$

*modulo*${\sim}$ is the D11: Set \begin{equation} X / {\sim} : = \{ {\sim}(x) : x \in X \} \end{equation}