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In set theory, the union (denoted by ∪) of a collection of sets is the set of all elements in the collection. [1] It is one of the fundamental operations through which sets can be combined and related to each other.
This article lists mathematical properties and laws of sets, involving the set-theoretic operations of union, intersection, and complementation and the relations of set equality and set inclusion. It also provides systematic procedures for evaluating expressions, and performing calculations, involving these operations and relations.
It is the algebra of the set-theoretic operations of union, intersection and complementation, and the relations of equality and inclusion. For a basic introduction to sets see the article on sets, for a fuller account see naive set theory, and for a full rigorous axiomatic treatment see axiomatic set theory.
Set theory is the branch of mathematical logic that studies sets, ... It is the set difference of the union and the intersection, (A ∪ B) \ (A ∩ B) or ...
In set theory and related branches of mathematics, a family (or collection) can mean, depending upon the context, any of the following: set, indexed set, multiset, or class. A collection F {\displaystyle F} of subsets of a given set S {\displaystyle S} is called a family of subsets of S {\displaystyle S} , or a family of sets over S ...
The simple theorems in the algebra of sets are some of the elementary properties of the algebra of union (infix operator: ∪), intersection (infix operator: ∩), and set complement (postfix ') of sets. These properties assume the existence of at least two sets: a given universal set, denoted U, and the empty set, denoted {}.
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
In mathematics, the symmetric difference of two sets, also known as the disjunctive union and set sum, is the set of elements which are in either of the sets, but not in their intersection. For example, the symmetric difference of the sets { 1 , 2 , 3 } {\displaystyle \{1,2,3\}} and { 3 , 4 } {\displaystyle \{3,4\}} is { 1 , 2 , 4 ...