In order for this relation to be an equivalence equation, it has to be reflexive, symmetric and transitive.

\textbf{Reflexive:}

All elements are related to themself

\[ DD, AA, CC, BB \]

\textbf{Symmetric:}

All relations has its symmetric counterpart

\begin{gather*}
CD\text{ and }DC
\end{gather*}

\textbf{Transitive:}

All pair of relations where $xRy$ and $yRz$ has its transitive counterpart

\begin{gather*}
DC\text{ and }CD\text{ with }DD \\
CD\text{ and }DC\text{ with }CC
\end{gather*}

Hence the relation is an equivalence relation