reflexive relation

A relationMathworldPlanetmathPlanetmath on a set A is reflexiveMathworldPlanetmathPlanetmathPlanetmathPlanetmath if and only if aa for all aA.

For example, let A={1,2,3}. Then {(1,1),(2,2),(3,3),(1,3),(3,2)} is a reflexive relation on A, because it contains (a,a) for all aA. However, {(1,1),(2,2),(2,3),(3,1)} is not reflexive because it does not contain (3,3).

On a finite setMathworldPlanetmath with n elements there are 2n2 relations, of which 2n2-n are reflexive.

Title reflexive relation
Canonical name ReflexiveRelation
Date of creation 2013-03-22 12:15:36
Last modified on 2013-03-22 12:15:36
Owner yark (2760)
Last modified by yark (2760)
Numerical id 17
Author yark (2760)
Entry type Definition
Classification msc 03E20
Related topic SymmetricPlanetmathPlanetmathPlanetmath
Related topic Transitive3
Related topic Antisymmetric
Related topic IrreflexiveMathworldPlanetmath
Defines reflexivity
Defines reflexive