Set partition

Let $X$ be a D11: Set.
A D11: Set $\mathcal{S} \subseteq \mathcal{P}(X)$ is a set partition of $X$ if and only if
 (1) $$X = \cup \mathcal{S}$$ D4984: Tight set cover (2) $$\forall \, E, F \in \mathcal{S} \left( E \neq F \quad \implies \quad E \cap F = \emptyset \right)$$ D1681: Disjoint set collection
Child definitions