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:
- A and B are disjoint.
- The intersection of A and B is the empty set.
- A ∩ B = {} (the same as the above, but in symbols).
We also say that a set U whose elements are themselves sets is mutually disjoint if its members are mutually disjoint. In symbols:
U is a partition of a set X if:- the union of U is X;
- U is mutually disjoint (as above); and
- {} does not belong to U.