Symmetric relation

Type of binary relation

A symmetric relation is a type of binary relation. A homogeneous relation R {\displaystyle R} on a set X {\displaystyle X} is symmetric if: for all a {\displaystyle a} and b {\displaystyle b} in X {\displaystyle X} , a R b {\displaystyle aRb} if and only if b R a {\displaystyle bRa} , where the notation a R b {\displaystyle aRb} means that the ordered pair ( a , b) {\displaystyle (a,b)} is in the relation R {\displaystyle R} . An example is the relation "is equal to", because if a = b is true then b = a is also true.

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