Category:Definitions/Pairwise Disjoint

This category contains definitions related to Pairwise Disjoint.
Related results can be found in Category:Pairwise Disjoint.

Set of Sets

A set of sets $\Bbb S$ is said to be pairwise disjoint if and only if:

$\forall X, Y \in \Bbb S: X \ne Y \implies X \cap Y = \O$

Here, $\cap$ denotes intersection, and $\O$ denotes the empty set.

Hence we can say that the elements of $\Bbb S$ are pairwise disjoint.

Family of Sets

An indexed family of sets $\family {S_i}_{i \mathop \in I}$ is said to be pairwise disjoint if and only if:

$\forall i, j \in I: i \ne j \implies S_i \cap S_j = \O$

Hence the indexed sets $S_i$ themselves, where $i \in I$, are referred to as being pairwise disjoint.