# Definition:Pairwise Disjoint

## Definition

### Set of Sets

A set of sets $\Bbb S$ is said to be pairwise disjoint iff:

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

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

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

### Family of Sets

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

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

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

## Also known as

Other names for pairwise disjoint include mutually disjoint and non-intersecting.