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Difference between revisions of "Symmetry (of a relation)"

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<table><TR><TD valign="top">[a1]</TD> <TD valign="top">  P.M. Cohn,  "Algebra" , '''1''' , Wiley  (1982)  pp. 17ff</TD></TR></table>
 
<table><TR><TD valign="top">[a1]</TD> <TD valign="top">  P.M. Cohn,  "Algebra" , '''1''' , Wiley  (1982)  pp. 17ff</TD></TR></table>
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[[Category:Logic and foundations]]

Latest revision as of 18:49, 19 October 2014

A property of a binary relation. A binary relation $R$ 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