Let $X_j$ be a D11: Set for each $j \in J$.
Then $X = \{ X_j \}_{j \in J}$ is a pairwise disjoint set collection if and only if \begin{equation} \forall \, i, j \in J \left( i \neq j \quad \implies \quad X_i \cap X_j = \emptyset \right) \end{equation}