In set theory, the complement of a set A, often denoted by A c {\displaystyle A^{c}} (or A′), is the set of elements not in A. When all elements in the...

set-theoretic operations of union, intersection, and complementation and the relations of set equality and set inclusion. It also provides systematic procedures...

In set theory, the union (denoted by ∪) of a collection of sets is the set of all elements in the collection. It is one of the fundamental operations...

Set theory is the branch of mathematical logic that studies sets, which can be informally described as collections of objects. Although objects of any...

of sets Boolean function Complement (set theory) Difference (set theory) Exclusive or Fuzzy set Intersection (set theory) Jaccard index List of set identities...

In the mathematical field of graph theory, the complement or inverse of a graph G is a graph H on the same vertices such that two distinct vertices of...

In set theory, the intersection of two sets A {\displaystyle A} and B , {\displaystyle B,} denoted by A ∩ B , {\displaystyle A\cap B,} is the set containing...

(sometimes called an antonym) Complement (group theory) Complementary subspaces Orthogonal complement Schur complement Complement (complexity), relating to...

Naive set theory is any of several theories of sets used in the discussion of the foundations of mathematics. Unlike axiomatic set theories, which are...

inversion, and complementation. Some theorists apply the methods of musical set theory to the analysis of rhythm as well. Although musical set theory is often...

order theory, a complemented lattice is a bounded lattice (with least element 0 and greatest element 1), in which every element a has a complement, i.e...

algebra of sets are some of the elementary properties of the algebra of union (infix operator: ∪), intersection (infix operator: ∩), and set complement (postfix...

In set theory, Zermelo–Fraenkel set theory, named after mathematicians Ernst Zermelo and Abraham Fraenkel, is an axiomatic system that was proposed in...

Class (set theory) Complement (set theory) Complete Boolean algebra Continuum (set theory) Suslin's problem Continuum hypothesis Countable set Descriptive...

In computational complexity theory, the complement of a decision problem is the decision problem resulting from reversing the yes and no answers. Equivalently...

"Set Theory", Stanford Encyclopedia of Philosophy, Metaphysics Research Lab, Stanford University Suppes, Patrick (1972) [1960], Axiomatic Set Theory,...

In mathematics, and particularly in set theory, category theory, type theory, and the foundations of mathematics, a universe is a collection that contains...

In measure theory, a conull set is a set whose complement is null, i.e., the measure of the complement is zero. For example, the set of irrational numbers...

Class (set theory) Complement (set theory) Complete Boolean algebra Continuum (set theory) Suslin's problem Continuum hypothesis Countable set Descriptive...

Borel set is Borel, not all analytic sets are Borel sets. A set is coanalytic if its complement is analytic. Many questions in descriptive set theory ultimately...

In mathematics, especially in the area of algebra known as group theory, a complement of a subgroup H in a group G is a subgroup K of G such that G = H...

are ubiquitous in modern mathematics. Indeed, set theory, more specifically Zermelo–Fraenkel set theory, has been the standard way to provide rigorous...

Neumann–Bernays–Gödel set theory (NBG) is an axiomatic set theory that is a conservative extension of Zermelo–Fraenkel–choice set theory (ZFC). NBG introduces...

the mathematical subdisciplines of order theory and abstract algebra. It consists of a partially ordered set in which every pair of elements has a unique...

computational complexity theory, decision problems are typically defined as formal languages, and complexity classes are defined as the sets of the formal languages...

In music theory, complement refers to either traditional interval complementation, or the aggregate complementation of twelve-tone and serialism. In interval...

empty set or void set is the unique set having no elements; its size or cardinality (count of elements in a set) is zero. Some axiomatic set theories ensure...

set theory (sometimes denoted by Z-), as set out in a seminal paper in 1908 by Ernst Zermelo, is the ancestor of modern Zermelo–Fraenkel set theory (ZF)...

Ramsey theory. A set is independent if and only if its complement is a vertex cover. Therefore, the sum of the size of the largest independent set α ( G...

relative complement. Borel sets are named after Émile Borel. For a topological space X {\displaystyle X} , the collection of all Borel sets on X {\displaystyle...