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Disjoint Sets

In mathematics and computer science, 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.

Explanation

Formally, two sets ''A'' and ''B'' are disjoint if their intersection is the empty set, i.e. if

:

A\cap B = \varnothing.\,

This definition extends to any collection of sets. A collection of sets is pairwise disjoint or mutually disjoint if any two sets in the collection are disjoint.

Formally, let ''I'' be an index set, and for each ''i'' in ''I'', let ''A''_''i'' be a set. Then the family of sets {''A''_''i'' : ''i'' ∈ ''I''} is pairwise disjoint if for any ''i'' and ''j'' in ''I'' with ''i'' ≠ ''j'',

:

A_i \cap A_j = \varnothing.\,

For example, the collection of sets { {1}, {2}, {3}, ... } is pairwise disjoint. If {''A''_''i''} is a pairwise disjoint collection (containing at least two sets), then clearly its intersection is empty:

:

\bigcap_{i\in I} A_i = \varnothing.\,

However, the converse is not true: the intersection of the collection
Source: Wikipedia