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:

${\displaystyle \forall a,b\in X(aRb\Leftrightarrow bRa),}$

where the notation ${\displaystyle aRb}$ means that ${\displaystyle (a,b)\in R}$.

If R^T represents the converse of R, then R is symmetric if and only if R = R^T.

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