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