---
title: "equivalence relation"
type: concept
related: [Predicates, Equivalence Relation]
source: https://www.jemoka.com/posts/kbhequivalence_relation/
confidence: high
status: active
---

a binary relation is an equivalence relation if
\(R\) is reflexive: \(xRx\) is true for all \(x\) \(R\) is symmetric: \(x R y\) is true implies \(y R x\) is true \(R\) is transitive: for every \(x,y,z\), \(xRy\) and \(y R z\) implies \(x R z\)
