Let $X$ be a D11: Set such that

(i)	\begin{equation} X \neq \emptyset \end{equation}
(ii)	$\mathcal{S} \subseteq \mathcal{P}(X)$ is a D83: Proper set partition for $X$

The proper set partition relation on $X$ with respect to $\mathcal{S}$ is the D4: Binary relation \begin{equation} \{ (x, y) \in X \times X : \exists \, S \in \mathcal{S} : x, y \in S \} \end{equation}