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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 symmetric difference of the sets A and B is commonly denoted by (alternatively, ), , or . It can be viewed as a form of addition modulo 2 . The power set of any set becomes an abelian group under the operation of symmetric difference, with the empty set as the neutral element of the group and every element in this group being its own ...
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.
Sets cannot have duplicate elements, [3] [4] so the union of the sets {1, 2, 3} ... operation on sets; Inclusion–exclusion principle – Counting technique in ...
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).
Of course, the inclusion-exclusion principle could be stated right away as a result from measure theory. The combinatorics formula follows by using the counting measure, the probability version by using a probability measure. However, counting is a very easy concept, so the article should start this way.
[3] [4] Kolmogorov axioms. 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 A ...