Quotient Space of Hausdorff Space is not necessarily Hausdorff

Theorem
Let $T = \left({S, \tau}\right)$ be a Hausdorff space.

Let $\mathcal R \subseteq S \times S$ be an equivalence relation on $S$.

Let $T_\mathcal R := \left({S / \mathcal R, \tau_\mathcal R}\right)$ be the quotient space of $S$ by $\mathcal R$.

Then $T_\mathcal R$ is not necessarily also a Hausdorff space.