A D4: Binary relation $B = (X \times Y, R)$ is symmetric if and only if $$\begin{equation} \forall \, x \in X : \forall \, y \in Y \left( (x, y) \in R \quad \implies \quad (y, x) \in R \right) \end{equation}$$

A D4: Binary relation $B = (X \times Y, R)$ is symmetric if and only if $$\begin{equation} \forall \, x \in X : \forall \, y \in Y \left( x R y \quad \implies \quad y R x \right) \end{equation}$$