# 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:

If *R*^{T} represents the converse of *R*, then *R* is symmetric if and only if *R* = *R*^{T}.^{[citation needed]}

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

By definition, a nonempty relation cannot be both symmetric and asymmetric (where if *a* is related to *b*, then *b* cannot be related to *a* (in the same way)). However, a relation can be neither symmetric nor asymmetric, which is the case for "is less than or equal to" and "preys on").

Symmetric and antisymmetric (where the only way *a* can be related to *b* and *b* be related to *a* is if *a* = *b*) are actually independent of each other, as these examples show.