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 $(a,b)\simeq (c,d)$, iff $ad=bc$. The the number of ordered pairs of the equivalence class of $(3,2)$ is

• A. $4$
• B. $5$
• C. $6$
• D. $7$

Answer 1

The correct option is C $6$

Let $(3,2)\cong (x,y)$

$\Rightarrow 3y=2x$

This is possible in the cases:

$x=3,y=2$

$x=6,y=4$

$x=9,y=6$

$x=12,y=3$

$x=15,y=10$

$x=18,y=12$

Hence total pairs are $6$.