Question

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

• A. 5
• B. 6
• C. 8
• D. 7

Answer 1

Answer: (D)

$A =\{2,3,4,5, \ldots,, 30\}$
$(a, b) \simeq(c, d) \Rightarrow a d=b c$
$(4,3) \simeq( c , d ) \Rightarrow 4 d =3 c$
$\Rightarrow \frac{4}{3}=\frac{ c }{ d }$
$\frac{ c }{ d }=\frac{4}{3}\,\,\&\,\,c , d \in\{2,3, \ldots \ldots, 30\}$
$( c , d )=\{(4,3),(8,6),(12,9),(16,12),(20,,15),(24,18),(28,21)\}$
No. of ordered pair $=7$