- $\forall X, Y \in \Bbb S: X \ne Y \implies X \cap Y = \varnothing$
Alternatively, we can say that the elements of $\Bbb S$ are pairwise disjoint.
- $\forall i, j \in I: i \ne j \implies S_i \cap S_j = \varnothing$
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.