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}

▾ Set of symbols

▾ Alphabet

▾ Deduction system

▾ Theory

▾ Zermelo-Fraenkel set theory

▾ Set

▾ Binary cartesian set product

▾ Binary relation

▾ Map

▾ Empty map

▾ Collection

▾ Minimally disjoint collection of sets

▾ N-wise disjoint set collection

▾ Alphabet

▾ Deduction system

▾ Theory

▾ Zermelo-Fraenkel set theory

▾ Set

▾ Binary cartesian set product

▾ Binary relation

▾ Map

▾ Empty map

▾ Collection

▾ Minimally disjoint collection of sets

▾ N-wise disjoint set collection

Formulation 0

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}

Then $X = \{ X_j \}_{j \in J}$ is a

Also known as

2-wise disjoint set collection