(i) | \begin{equation} X \neq \emptyset \end{equation} |

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

**equivalence class**of $x \in X$ with respect to ${\sim}$ is the D11: Set \begin{equation} \{ y : (x, y) \in {\sim} \} \end{equation}