Question

Let $A=\{2,3,4,5,...,17,18\}.$ Let $\simeq$ be the equivalence relation on $A\times A,$ cartesian product of $A$ with itself, defined by $(a,b)\simeq (c,d)$ if $ad=bc.$ Then the number of ordered pairs of the equivalence class of $(3,2)$ is

Answer 1

The number of ordered pairs in the equivalence class of $(3,2)$ is the number of ordered pairs $(a,b)$ satisfying $(a,b)\simeq (3,2)$ i.e.
$2a=3b\Rightarrow \frac{a}{b}=\frac{3}{2}$
$\therefore$ Ordered pairs are $(3,2),(6,4),(9,6),(12,8),(15,10),(18,12)$