Namespaces
Variants
Actions

Symmetry (of a relation)

From Encyclopedia of Mathematics
Jump to: navigation, search

A property of a binary relation. A binary relation on a set A is called symmetric if for any pair of elements a,b \in A, aRb implies b R a, i.e. R \subseteq R^{-1}. An example of a symmetric relation is an Equivalence relation.


Comments

An anti-symmetric relation on a set A is a reflexive relation R such that R \cap R^{-1} \subseteq \Delta = \{ (x,x) : \forall x \in A \}.

References

[a1] P.M. Cohn, "Algebra" , 1 , Wiley (1982) pp. 17ff
How to Cite This Entry:
Symmetry (of a relation). Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Symmetry_(of_a_relation)&oldid=33962
This article was adapted from an original article by T.S. Fofanova (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article