Search results
Results from the WOW.Com Content Network
Inclusion–exclusion illustrated by a Venn diagram for three sets. Generalizing the results of these examples gives the principle of inclusion–exclusion. To find the cardinality of the union of n sets: Include the cardinalities of the sets. Exclude the cardinalities of the pairwise intersections.
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.
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 is a partial order: Explicitly, this means that inclusion, which is a binary operation, has the following three properties: [3] Reflexivity : L ⊆ L {\textstyle L\subseteq L} Antisymmetry : ( L ⊆ R and R ⊆ L ) if and only if L = R {\textstyle (L\subseteq R{\text{ and }}R\subseteq L){\text{ if and only if }}L=R}
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
In probability theory, the coupon collector's problem refers to mathematical analysis of "collect all coupons and win" contests. It asks the following question: if each box of a given product (e.g., breakfast cereals) contains a coupon, and there are n different types of coupons, what is the probability that more than t boxes need to be bought ...
The subset sum problem (SSP) is a decision problem in computer science. In its most general formulation, there is a multiset S {\displaystyle S} of integers and a target-sum T {\displaystyle T} , and the question is to decide whether any subset of the integers sum to precisely T {\displaystyle T} . [ 1 ]
For example, the symmetric difference of the sets {,,} and {,} is {,,}. The symmetric difference of the sets A and B is commonly denoted by A Δ B {\displaystyle A\operatorname {\Delta } B} (alternatively, A B {\displaystyle A\operatorname {\vartriangle } B} ), A ⊕ B {\displaystyle A\oplus B} , or A ⊖ B {\displaystyle A\ominus B} .