Definition:Inverse Relation

From ProofWiki
Jump to navigation Jump to search

Definition

Let $\RR \subseteq S \times T$ be a relation.


The inverse relation to (or of) $\RR$ is defined as:

$\RR^{-1} := \set {\tuple {t, s}: \tuple {s, t} \in \RR}$


That is, $\RR^{-1} \subseteq T \times S$ is the relation which satisfies:

$\forall s \in S: \forall t \in T: \tuple {t, s} \in \RR^{-1} \iff \tuple {s, t} \in \RR$


Also known as

An inverse relation is also seen as converse relation.


Some sources use the notation $\RR^t$, for example 1975: T.S. Blyth: Set Theory and Abstract Algebra.

Others use $\breve {\RR}$, for example 1946: Alfred Tarski: Introduction to Logic and to the Methodology of Deductive Sciences (2nd ed.) and 1940: Garrett Birkhoff: Lattice Theory.


Also see

  • Results about inverse relations can be found here.


Sources

Retrieved from "https://proofwiki.org/w/index.php?title=Definition:Inverse_Relation&oldid=463610"