The union of two sets and is the set obtained by combining the members of each. This is written , and is pronounced " union " or " cup ." The union of sets through is written . The union of a list may be computed in the Wolfram Language as Union[l].
Let , , , ... be sets, and let denote the probability of . Then
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Similarly,
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The general statement of this property for sets is known as the inclusion-exclusion principle.
If and are disjoint sets, then by definition , so
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Continuing, for a set of disjoint elements , , ...,
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which is the countable additivity probability axiom. Now let
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then
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