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Confluence (term rewriting), discusses several unusual but fundamental properties of binary relations; Correspondence (algebraic geometry), a binary relation defined by algebraic equations; Hasse diagram, a graphic means to display an order relation; Incidence structure, a heterogeneous relation between set of points and lines
Pages in category "Properties of binary relations" The following 22 pages are in this category, out of 22 total. This list may not reflect recent changes. A.
Various properties of relations are investigated. A relation R is reflexive if xRx holds for all x, and irreflexive if xRx holds for no x. It is symmetric if xRy always implies yRx, and asymmetric if xRy implies that yRx is impossible. It is transitive if xRy and yRz always implies xRz.
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.
Properties of binary relations (4 C, 22 P) Pages in category "Binary relations" The following 26 pages are in this category, out of 26 total.
An asymmetric relation need not have the connex property. For example, the strict subset relation is asymmetric, and neither of the sets {,} and {,} is a strict subset of the other. A relation is connex if and only if its complement is asymmetric.
Formally, a partial order is a homogeneous binary relation that is reflexive, antisymmetric, and transitive. A partially ordered set ( poset for short) is an ordered pair P = ( X , ≤ ) {\displaystyle P=(X,\leq )} consisting of a set X {\displaystyle X} (called the ground set of P {\displaystyle P} ) and a partial order ≤ {\displaystyle \leq ...
A logical matrix, binary matrix, relation matrix, Boolean matrix, or (0, 1)-matrix is a matrix with entries from the Boolean domain B = {0, 1}. Such a matrix can be used to represent a binary relation between a pair of finite sets. It is an important tool in combinatorial mathematics and theoretical computer science.