[[Class]]
# Relation class

A **relation class** is a generalization of a [[Relation set]]. #m/def/set
When working in a [[material set theory]] with [[Class|classes]], one may more widely consider a (binary) **relation** as any subset of the [[Cartesian product#Cartesian product of classes]] $V \times V$ where $V$ is the [[Complement Axiom for classes|universal class]], and we write
$$
\begin{align*}
\rhood(X) \iff X \sube V^2
\end{align*}
$$
In a material set theory without classes like [[ZF]] one may still treat this indirectly, by a [[predicative formula]] with two arguments.
The [[Class existence theorem schema]] gives a sense in which these conceptions are equivalent in [[NBG]].

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#state/tidy | #SemBr  | #lang/en