Disjoint sets

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Two sets 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, while $\{1, 2, 3\}$ and $\{2, 4, 6\}$ 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 $\{1, 2\}$, $\{3, 4\}$ and $\{5, 6\}$ are pairwise disjoint. Alternatively, one can ask for the weaker condition that the sets have empty intersection. For instance, the three sets $\{1, 2\}$, $\{1, 3\}$ and $\{2, 4\}$ have empty intersection but are not pairwise disjoint.

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