Symmetric relation

A symmetric relation is a type of binary relation. An example is the relation "is equal to", because if a = b is true then b = a is also true. Formally, a binary relation R over a set X is symmetric if:

[1]

where the notation means that .

If RT represents the converse of R, then R is symmetric if and only if R = RT.[citation needed]

Symmetry, along with reflexivity and transitivity, are the three defining properties of an equivalence relation.[1]


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