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...

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...

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 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...

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...

Aggregate complementation, the separation of pitch-class collections into complementary sets Complementary color, in the visual arts Complement system (immunology)...

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

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...

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

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...

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...

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

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

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...

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...

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

intersection, and relative complement. Borel sets are named after Émile Borel. For a topological space X, the collection of all Borel sets on X forms a σ-algebra...

elements, called the empty set; a set with a single element is a singleton. Sets are ubiquitous in modern mathematics. Indeed, set theory, more specifically Zermelo–Fraenkel...

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...

In set theory and its applications throughout mathematics, a class is a collection of sets (or sometimes other mathematical objects) that can be unambiguously...

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...

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

Probability theory – Branch of mathematics concerning probability Ring of sets – Family closed under unions and relative complements Set function – Function...

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

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...