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Inclusion Exclusion Core Form

Inclusion Exclusion Core Form

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we can represent three finite sets a b and c by the Venn diagram shown here now suppose we want to find the cardinality or the number of elements in the union a union B Union C to do this we start by taking the number of elements in a and adding that to the number of elements in B and adding that to the number of elements in C unfortunately this is too much because we've over counted the elements in A and B so we remove the cardinality of a intersect B likewise we need to remove the cardinality of a intersect C since we've counted those elements twice and we need to subtract the cardinality of B intersect C since we've counted those elements twice but now notice that the elements that are in the intersection of all three sets have been added three times and subtracted three times so we need to re-add the cardinality of a intersect B intersect C this formula is known as the three set inclusion exclusion formula

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