Question

Let $A=\{1,2,3,4,6\}.$ Let $R$ be the relation on $A$ defined by $\left\{\right(a,b):a,b\in A,b$ is exactly divisible by $a\}$
$\left(i\right)$ Write $R$ in roster form
$\left(ii\right)$ Find the domain of $R$
$\left(iii\right)$ Find the range of $R$

Answer 1

Given
$A=\{1,2,3,4,6\}$
$R=\left\{\right(a,b):a,b\in A,b$ is exactly divisible by $a\}$

$\left(i\right)R$ in roster form
$R=\left\{\right(1,1),(1,2),(1,3),(1,4),(1,6),(2,2),(2,4),(2,6),(3,3),(3,6),(4,4),(6,6\left)\right\}$

$\left(ii\right)$ Domain of $R$
The domain of $R$ is the set of all first elements of ordered pairs in relation $R$.
Hence, domain of $R=A=\{1,2,3,4,6\}$

$\left(iii\right)$ Range of $R$
The range of $R$ is the set of second elements in relation $R$.
Hence, range of $R=\{1,2,3,4,6\}$