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(→Inclusion-Exclusion Principle (Basic)) |
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Let B and C be subsets of a given set A. To count the number of elements in the union of B and C, we must evaluate the following: | Let B and C be subsets of a given set A. To count the number of elements in the union of B and C, we must evaluate the following: | ||
| − | <math> |B \cup C| = |B| + |C| - |B \cap C| | + | <math> |B \cup C| = |B| + |C| - |B \cap C| <math\> |
| + | |||
| + | Subtracting <math>|B \cap C| <math\> corrects the overcount. | ||
Revision as of 06:46, 7 September 2008
Inclusion-Exclusion Principle (Basic)
Let B and C be subsets of a given set A. To count the number of elements in the union of B and C, we must evaluate the following:
$ |B \cup C| = |B| + |C| - |B \cap C| <math\> Subtracting <math>|B \cap C| <math\> corrects the overcount. $
