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Disjoint sets

In mathematics, two sets are said to be disjoint if they have no element in common. For example, {1,2,3} and {4,5,6} are disjoint sets.

The following statements are logically equivalent:

Given several sets, we say they are mutually disjoint or pairwise disjoint if any two of the sets in question are disjoint. For example, the sets {1,2,3}, {4,5,6}, and {7,8,9} are mutually disjoint. However, {1,2,3}, {4,5,6}, and {3,4} are not mutually disjoint, even though there is no element that belongs to all of them.

We also say that a set U whose elements are themselves sets is mutually disjoint if its members are mutually disjoint. In symbols:

For any A,B in U, A = B or AB = {}.

U is a partition of a set X if: