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Venn diagram showing the union of sets A and B as everything not in white. In combinatorics, the inclusion–exclusion principle is a counting technique which generalizes the familiar method of obtaining the number of elements in the union of two finite sets; symbolically expressed as
The inclusion–exclusion principle relates the size of the union of multiple sets, the size of each set, and the size of each possible intersection of the sets. The smallest example is when there are two sets: the number of elements in the union of A and B is equal to the sum of the number of elements in A and B , minus the number of elements ...
The inclusion-exclusion principle for two finite sets states that the size of their union is the sum of the sizes of the sets minus the size of their intersection. The inclusion–exclusion principle is a technique for counting the elements in a union of two finite sets in terms of the sizes of the two sets and their intersection.
In the general case, for a word with n 1 letters X 1, n 2 letters X 2, ..., n r letters X r, it turns out (after a proper use of the inclusion-exclusion formula) that the answer has the form () , for a certain sequence of polynomials P n, where P n has degree n.
Inclusion–exclusion principle – Counting technique in combinatorics; Intersection (set theory) – Set of elements common to all of some sets; Iterated binary operation – Repeated application of an operation to a sequence; List of set identities and relations – Equalities for combinations of sets; Naive set theory – Informal set theories
An extension of the addition law to any number of sets is the inclusion–exclusion principle. Setting B to the complement A c of A in the addition law gives ...
The Oscars unveiled new guidelines this week that are designed to promote diversity and inclusion both in front of and behind the camera. But the rules are inspiring confusion and controversy as ...
There is an inclusion–exclusion principle for finite multisets (similar to the one for sets), stating that a finite union of finite multisets is the difference of two sums of multisets: in the first sum we consider all possible intersections of an odd number of the given multisets, while in the second sum we consider all possible ...