In order for this relation to be a partial order, it has to be reflexive, antisymmetric and transitive.

\textbf{Reflexive:}

All elements are related to themself

\[ AA, BB, CC, DD \]

\textbf{Antisymmetric:}

No relation have a symmetric counterpart \\

(Listing the ones that don't have a symmetric counterpart would just be listing the whole set) \\

\textbf{Transitive:}

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

\begin{gather*}
AB\text{ and }BD\text{ with }AD \\
AB\text{ and }BC\text{ with }AC \\
BC\text{ and }CD\text{ with }BD \\
AC\text{ and }CD\text{ with }AD
\end{gather*}

Hence the relation is a partial order