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: where the notation formula_2 means that formula_3. If "R" represents the converse of "R", then "R" is symmetric if and only if "R" = "R". Symmetry, along with reflexivity and transitivity, are the three defining properties of an equivalence relation. Relationship to asymmetric and antisymmetric relations. 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.