Relations on a set

$\newcommand{\N}{\mathbb N} \newcommand{\Z}{\mathbb Z} \newcommand{\Q}{\mathbb Q} \newcommand{\R}{\mathbb R} \newcommand{\lt}{<} \newcommand{\gt}{>} \newcommand{\amp}{&} \definecolor{fillinmathshade}{gray}{0.9} \newcommand{\fillinmath}[1]{\mathchoice{\colorbox{fillinmathshade}{$\displaystyle \phantom{\,#1\,}$}}{\colorbox{fillinmathshade}{$\textstyle \phantom{\,#1\,}$}}{\colorbox{fillinmathshade}{$\scriptstyle \phantom{\,#1\,}$}}{\colorbox{fillinmathshade}{$\scriptscriptstyle\phantom{\,#1\,}$}}} $

Section 5.2 Relations on a set

When $A = B$ we refer to the relation as a relation on $A\text{.}$

Consider the set $A = \{2,3,4,6,8\}\text{.}$ Let’s define a relation $R$ on $A$ such that $aRb$ iff $a | b$ ($a$ divides $b$). The relation $R$ can be represented by the set of ordered pairs where the first element divides the second:

Prev Top Next