Let $A=\{2,3,4,5, \ldots, 30\}$ and ' $\simeq$ 'be an equivalence relation on $A imes A$, defined

Question

Let $A=\{2,3,4,5, \ldots, 30\}$ and ' $\simeq$ 'be an equivalence relation on $A 	imes A$, defined by $(a, b) \simeq(c, d)$ if and only if $a d=b c$. Then the number of ordered pairs which satisfy this equivalence relation with ordered pair $(4,3)$ is equal to\

Professor PC Thomas Classes · Answer

(c) : $(a, b) \simeq(c, d) \Leftrightarrow a d=b c$\ $\Rightarrow \frac{a}{c}=\frac{b}{d} \Rightarrow \frac{4}{c}=\frac{3}{d} \Rightarrow \frac{c}{d}=\frac{4}{3}$\ $(c, d) \in(2,3,4, \ldots, 30)$\ $	herefore \quad(c, d)=(4,3),(8,6),(12,9),(16,12)$, $(20,15),(24,18),(28,21)$\ $	herefore \quad 7$ ordered pair exist.\