Search results
Results from the WOW.Com Content Network
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. A nullary union refers to a union of zero ( ) sets and it is by definition equal to the empty set.
The complement of the union of two sets is the same as the intersection of their complements; The complement of the intersection of two sets is the same as the union of their complements; or not (A or B) = (not A) and (not B) not (A and B) = (not A) or (not B)
Just as arithmetic features binary operations on numbers, set theory features binary operations on sets. [6] The following is a partial list of them: Union of the sets A and B, denoted A ∪ B, is the set of all objects that are a member of A, or B, or both. [7] For example, the union of {1, 2, 3} and {2, 3, 4} is the set {1, 2, 3, 4}.
Fundamentals. The algebra of sets is the set-theoretic analogue of the algebra of numbers. Just as arithmetic addition and multiplication are associative and commutative, so are set union and intersection; just as the arithmetic relation "less than or equal" is reflexive, antisymmetric and transitive, so is the set relation of "subset".
Three sets involved. [edit] In the left hand sides of the following identities, L{\displaystyle L}is the L eft most set, M{\displaystyle M}is the M iddle set, and R{\displaystyle R}is the R ight most set. Precedence rules. There is no universal agreement on the order of precedenceof the basic set operators.
Inclusion–exclusion principle. In combinatorics, a branch of mathematics, 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. where A and B are two finite sets and | S | indicates the cardinality of a ...
The combined region of the two sets is called their union, denoted by A ∪ B, where A is the orange circle and B the blue. [2] The union in this case contains all living creatures that either are two-legged or can fly (or both). The region included in both A and B, where the two sets overlap, is called the intersection of A and B, denoted by A ...
Compared to the classical counterpart, one is generally less likely to prove the existence of relations that cannot be realized. A restriction to the constructive reading of existence apriori leads to stricter requirements regarding which characterizations of a set involving unbounded collections constitute a (mathematical, and so always meaning total) function.