Dr. J’s Guide to Partitions

Dr. J introduces a property the set properties of disjoint, pairwise disjoint, and partition. Two sets are disjoint if their intersection is the empty set. A collection of sets is pairwise disjoint if every pair of sets is disjoint. A collection of sets is a partition of S if 1) none of the sets is the empty set (this is not strictly necessary but eliminates trivial situations, 2) the collection is pairwise disjoint, and 3) the union of the sets in the collection is S.

A number of examples are provided as well as Venn Diagrams for each of these properties.