First slide

Relations XII

Question

Let A = {2,3,4,……..30} and $≃$ be an equivalence relation on A $\times$ A , defined by $(a, b) ≃ (c, d)$ , 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

Moderate

Solution

A = {2,3,4,……..30}
$(a, b) ≃ (c, d)$
$(4, 3) ≃ (c, d)$
$\frac{4}{3} = \frac{c}{d}$
$\frac{c}{d} = \frac{4}{3}$ and $c, d \in \{2, 3, . . . . . 30\}$
$\Rightarrow$ (c ,d)={(4,3),(8,6),(12,9),(16,12),(20,15),(24,18),(28,21)}
no.of ordered pairs=7

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