The quotient of $X$ by $R$ is the set $X/\mathord {\sim }_{R}$ defined by
\[ X/\mathord {\sim }_{R}\mathrel {\smash {\overset {\mathclap {\scriptscriptstyle \text{def}}}=}}\webleft\{ \webleft [a\webright ]\in \mathcal{P}\webleft (X\webright )\ \middle |\ a\in X\webright\} . \]
