Definition:Pairwise Disjoint

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Definition

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.


Also known as

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

Some sources hyphenate: pair-wise.


Also see


Sources