Equivalence Relations

Equivalence Relations

An Equivalence Relation \(R\) between two sets \(A\) and \(B\) is a subset of \(A\times B\), such that \(R\) is:

Reflexive

\[ a R a \]

Symmetric

\[ a R b \implies b R a\]

Transitive

\[ a R b \text{ and } b R c \implies a R c \]