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  • Let A = { 2,3,4,5 ...., 30} and  be an equivalence relation on , defined by <img alt="(a,b)\simeq (c,d)" src="

Let A = { 2,3,4,5 ...., 30} and '\simeq ' be an equivalence relation on A \times A, defined by (a,b)\simeq (c,d), if only and only ad = bc. Then the number of ordered pairs which satisfy this equivalence relation with ordered pair (4,3) is equal to:
Option: 1 8
Option: 2 5
Option: 3 7
Option: 4 6

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best_answer

 

\begin{aligned} &A =\{2,3,4,5, \ldots ., 30\} \\ &( a , b ) \simeq( c , d ) \quad \Rightarrow \quad ad = bc \\ &(4,3) \simeq( c , d ) \quad \Rightarrow \quad 4 d =3 c \\ &\Rightarrow \frac{4}{3}=\frac{ c }{ d } \end{array}

\begin{aligned} &\frac{ c }{ d }=\frac{4}{3} \quad \&\quad c , d \in\{2,3, \ldots \ldots, 30\}\\ &( c , d )=\{(4,3),(8,6),(12,9),(16,12),(20,\\ &\text { 15), }(24,18),(28,21)\}\\ &\text { No. of ordered pair }=7 \end{aligned}

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