Definition:Pairwise Disjoint/Set of Sets

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Definition

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.

Also known as

Such a set of sets, whose elements are pairwise disjoint, is often referred to as a pairwise disjoint collection.

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