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.
The binary operations of set union () and intersection () satisfy many identities. Several of these identities or "laws" have well established names.
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properties and laws ofsets, involving the set-theoretic operations of union, intersection, and complementation and the relationsofset equality andset inclusion...
calculus identitiesListof inequalities Listofsetidentitiesandrelations – Equalities for combinations ofsets A Collection of Algebraic Identities Matrix...
sets, the set-theoretic operations of union, intersection, and complementation and the relationsofset equality andset inclusion. It also provides systematic...
displaying wikidata descriptions as a fallback Listofsetidentitiesandrelations – Equalities for combinations ofsets Munkres 2000, p. 91. Bartle, Robert G...
these are identities involving certain functions of one or more angles. They are distinct from triangle identities, which are identities potentially...
Exclusive or Fuzzy set Intersection (set theory) Jaccard index Listofsetidentitiesandrelations Logical graph Separable sigma algebras Set theory Symmetry...
Hyperarithmetical set Analytical set Analytic set, Coanalytic set Suslin set Projective set Inhabited set Multiset Listofsetidentitiesandrelations – Equalities...
map) if and only if the same is true of f : ( X , τ f ) → Y . {\displaystyle f:\left(X,\tau _{f}\right)\to Y.} Listofsetidentitiesandrelations – Equalities...
List of set identitiesandrelations – Equalities for combinations ofsets Partition of a set – Mathematical ways to group elements of a set Sum type –...
be a set S equipped with a binary operation ∗. Then an element e of S is called a left identity if e ∗ s = s for all s in S, and a right identity if s...
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A (typically binary operations such as addition and multiplication), and a finite setofidentities, known as axioms, that these operations must satisfy...
operations on sets. The following is a partial listof them: Union of the sets A and B, denoted A ∪ B, is the setof all objects that are a member of A, or B...
diagram, also called a set diagram or logic diagram, shows all possible logical relations between a finite collection of different sets. These diagrams depict...
in the eyes of others and themselves. Identities are formed on many levels. The micro-level is self-definition, relations with people, and issues as seen...
consistency relations among the maps dn,i and sn,i. Rather than requiring these simplicial identities explicitly as part of the definition, the short and elegant...