Editing Binary relation (section)

=== Converse ===
{{main|Converse relation}}
{{see also|Duality (order theory)}}
If <math>R</math> is a binary relation over sets <math>X</math> and <math>Y</math> then <math>R^\textsf{T} = \{ (y, x) \mid xRy \}</math> is the {{em|converse relation}},<ref>[[Garrett Birkhoff]] & Thomas Bartee (1970) ''Modern Applied Algebra'', page 35, McGraw-Hill</ref> also called {{em|inverse relation}},<ref>[[Mary P. Dolciani]] (1962) ''Modern Algebra: Structure and Method'', Book 2, page 339, Houghton Mifflin</ref> of <math>R</math> over <math>Y</math> and <math>X</math>.

For example, <math>=</math> is the converse of itself, as is <math>\neq</math>, and <math><</math> and <math>></math> are each other's converse, as are <math>\leq</math> and <math>\geq.</math> A binary relation is equal to its converse if and only if it is [[Symmetric relation|symmetric]].