Relation

• Definition: A relation betwen two sets $A$ and $B$ is any Subset of the Cartesian Product $A\times B$.
• Notation:

$$R\supseteq A\times B$$

• Meaning: A relation pairs elements of $A$ with elements of $B$, possibly in many-to-many ways.
• Examples:
  • “is less than”: $R=\{(x,y)\in \mathbb{N}\times \mathbb{N}\mid x<y\}$
  • “is a divisor of “: $R=\{(x,y)\in \mathbb{Z}\times \mathbb{Z}\mid x|y\}$