The equivalence class associated to $a$ is the set $\webleft [a\webright ]$ defined by
\begin{align*} \webleft [a\webright ] & \mathrel {\smash {\overset {\mathclap {\scriptscriptstyle \text{def}}}=}}\left\{ x\in X\ \middle |\ x\sim _{R}a\right\} \\ & = \left\{ x\in X\ \middle |\ a\sim _{R}x\right\} \tag {since $R$ is symmetric}.\end{align*}
