If $R$ is open equivalence then $Rx$ is closed?

Question

Let $R$ be an equivalence relation on topological space $X$. "Suppose $R$ is open.(i.e. $\forall x\in X, Rx$ is open.) Then $Rx$ is closed."

$\textbf{Q:}$ Why is $Rx$ closed and open?

Ref: Profinite Groups Chpt 1, pg 10. by Luis Ribes, Pavel Zalesski.

Answer 1

Hint: Show: $$Rx=\left(\bigcup\limits_{y\,\mid\,(y,x)\notin R} Ry\right)^{c}.$$