Please Login to access more options.
Definition (Equivalence Relation And Equivalence Class)
Let $R$ be a relation on a set $A$.
- We say that $R$ is an equivalence relation on $A$ if and only if $R$ is reflexive, symmetric, and transitive.
- If $R$ is an equivalence relation on $A$ and $a\in A$, then the equivalence class of $a$ is the set of all elements $b$ such that $(a,b)\in R$. We denote the equivalence class of $a$ by $$[a]=\{b\in A\mid (a,b)\in R\}.$$