Difference between revisions of "Disjoint sets"
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| − | Two | + | Two [[set]]s are said to be '''disjoint''' if they have no [[element]] in common. For example, |
| − | {1,2,3,4} and {5,6,7,8} are disjoint sets. | + | <math>\{1,2,3,4\}</math> and <math>\{5,6,7,8\}</math> are disjoint sets, while <math>\{1, 2, 3\}</math> and <math>\{2, 4, 6\}</math> are not disjoint. |
| − | + | Disjointness can be generalized to several sets in more than one way. One possibility is the notion of ''pairwise disjoint'': a number of sets are pairwise disjoint if every pair of the sets are disjoint. For example, the three sets <math>\{1, 2\}</math>, <math>\{3, 4\}</math> and <math>\{5, 6\}</math> are pairwise disjoint. Alternatively, one can ask for the weaker condition that the sets have [[empty set | empty]] [[intersection]]. For instance, the three sets <math>\{1, 2\}</math>, <math>\{1, 3\}</math> and <math>\{2, 4\}</math> have empty intersection but are not pairwise disjoint. | |
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Latest revision as of 12:38, 29 October 2006
Two sets are said to be disjoint if they have no element in common. For example,
and 
are disjoint sets, while 
and 
are not disjoint.
Disjointness can be generalized to several sets in more than one way. One possibility is the notion of pairwise disjoint: a number of sets are pairwise disjoint if every pair of the sets are disjoint. For example, the three sets 
, 
and 
are pairwise disjoint. Alternatively, one can ask for the weaker condition that the sets have empty intersection. For instance, the three sets , 
and 
have empty intersection but are not pairwise disjoint.
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