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Symmetric Relation




In Mathematical Notation , this is:

: orall a, b \in X,\ a R b \Rightarrow \; b R a

Note: symmetry is '''not''' the exact opposite of '' Antisymmetry '' (''aRb'' and ''bRa'' implies ''b'' = ''a''). There are relations which are both symmetric and antisymmetric (for example, Equality ), there are relations which are neither symmetric nor antisymmetric ( Divisibility ), there are relations which are symmetric and not antisymmetric ( Congruence Modulo ''n''), and there are relations which are not symmetric but are anti-symmetric ("is less than or equal to"). Also, the empty relation is, Vacuously , both symmetric and asymmetric.


PROPERTIES CONTAINING THE SYMMETRIC RELATION

Equivalence Relation - A symmetric relation that is also Transitive and Reflexive .


EXAMPLES


  • "is married to" is a symmetric relation, while "is less than" is not.

  • "is equal to" ( Equality )

  • "... is odd and ... is odd too":

  • ::::::



SEE ALSO