Definition:Pairwise Disjoint/Set of Sets

Definition
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.

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.