ThmDex – An index of mathematical definitions, results, and conjectures.
Set of symbols
Deduction system
Zermelo-Fraenkel set theory
Binary cartesian set product
Binary relation
Definition D5348
Set of binary relations
Formulation 0
Let $X$ and $Y$ each be a D11: Set such that
(i) $X \times Y$ is the D191: Binary cartesian set product of $(X, Y)$
The set of binary relations on $X \times Y$ is the D11: Set \begin{equation} \{ R : R \subseteq X \times Y \} \end{equation}
Number of binary relations on a finite set
Number of binary relations on binary cartesian product