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# Difference betweenDisjoint sets and pairwise disjoint sets?

Updated: 4/28/2022

Wiki User

12y ago

Assuming that, by 'disjoint', you mean that a collection of sets has an empty intersection, here is the difference between pairwise disjoint and 'disjoint':

If a collection of sets is pairwise disjoint, it implies that the collection is 'disjoint': If no two sets overlap, then no k sets would overlap for any k, since this would require the overlap of at least two sets i.e. you know for sure that k things aren't in contact at a common point if you know that no two of them are in contact with each other.

However, if a collection of sets is 'disjoint' (so the overall intersection is empty), it doesn't mean that the collection is pairwise disjoint. For instance, you could have a collection of 4 sets containing two overlapping pairs, where no set in one pair overlaps with a set in the other. So the intersection of the whole thing would be empty without pairwise disjointness. You could have a few things in contact with each other without all of them sharing a point of contact.

Wiki User

12y ago