Example 1

Let $\mathrm{R}$ be the equivalence relation "$x \in \mathrm{E}$ and $y \in \mathrm{E}$ and $x = y$" on a set $\mathrm{E}$. The equivalence class of $x \in \mathrm{E}$ is then the set $\{x\}$, and the canonical mapping $x \to \{x\}$ of $\mathrm{E}$ onto $\mathrm{E}/\mathrm{R}$ is bijective.