Disjoint set
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.
Formally, two sets A and B are disjoint if their intersection is empty, i.e. if
This definition extends to any collection of sets. A collection of sets is pairwise disjoint or mutually disjoint if any two distinct sets in the collection are disjoint.
Formally, let I be an index set, and for each i in I, let Ai be a set. Then the collection of sets {Ai : i in I} is pairwise disjoint if for any i and j in I,
For example, the collection of sets is pairwise disjoint. If {Ai} is a pairwise disjoint collection, then clearly its intersection is empty:
However, the converse is not true -- the intersection of the collection is empty, but the collection is not pairwise disjoint.
A collection of sets {Ai : i in I} is a partition of the set X if {Ai} is a pairwise disjoint collection not containing the empty set, and if
See also:
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