Relations (Sets)

Definition

A relation $R$ from the elements of set $A$ to the elements of set $B$ is a subset of $A \times B$.

…alternatively…

Let $A$ and $B$ be two non-empty sets, then every subset of $A \times B$ defines a relation from $A$ to $B$ and ever relation from $A$ to $B$ is a subset of $A \times B$.

Let $R \subseteq A \times B$ and $(a, b) \in R$. Then we say that $a$ is related to $b$ by the relation $R$ and write it as $a R b$. If $(a, b) \in R$, we write it as $a R b$