Properties of a relation R

A relation R on a set relates some pairs. We write $a R b$ when $a$ is related to $b$.

R is reflexive if $a R a$ for every $a$. It is symmetric if $a R b \Rightarrow b R a$. It is transitive if $a R b$ and $b R c$ give $a R c$.

A relation with all three properties is an equivalence relation.