Let $A=\{7,8,9\}$ and $B=\{1,2,3\}.$ Define a relation $R$ from $A$ to $B$ as follows:

For all $(x,y)inAB,(x,y)inR$ if and only if $\frac{x}{y+1}$ is an integer.

$($a$)$ Write $AB$ in set$-$roster notation

$($b$)$ Determine the validity of the following:

i$.$ Is $9R2?$

ii$.$ Is $(8,3)inR?$

$($c$)$ Write $R$ as a set of ordered pairs.

$($d$)$ Identify the domain and co$-$domain of $R.$

$($e$)$ Is $R$ a function, explain.