Editing Symmetric relation (section)

== Properties ==
* A symmetric and [[transitive relation]] is always [[quasireflexive relation|quasireflexive]].{{efn|If ''xRy'', the ''yRx'' by symmetry, hence ''xRx'' by transitivity. The proof of {{nowrap|''xRy'' ⇒ ''yRy''}} is similar.}}
* One way to count the symmetric relations on ''n'' elements, that in their binary matrix representation the upper right triangle determines the relation fully, and it can be arbitrary given, thus there are as many symmetric relations as {{nowrap|''n'' × ''n''}} binary upper triangle matrices, 2<sup>''n''(''n''+1)/2</sup>.{{refn|{{Cite OEIS|A006125}}}}

{{Number of relations}}