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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
Principe d'inclusion-exclusion; Usage on gl.wikipedia.org Principio de inclusión-exclusión; Usage on hu.wikipedia.org Matematika; Szitaformula; Usage on it.wikipedia.org Principio di inclusione-esclusione; Usage on ko.wikipedia.org 포함배제의 원리; Usage on nl.wikipedia.org Principe van inclusie en exclusie; Usage on pl.wikipedia.org
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 ...
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
A series of Venn diagrams illustrating the principle of inclusion-exclusion.. The inclusion–exclusion principle (also known as the sieve principle [7]) can be thought of as a generalization of the rule of sum in that it too enumerates the number of elements in the union of some sets (but does not require the sets to be disjoint).
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.
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Venn diagram; Tree diagram; The ... An extension of the addition law to any number of sets is the inclusion–exclusion principle. Setting B to the complement A c of ...