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GO Classes DPP | GATE CS | Discrete Mathematics| Set Theory

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Let $A=\{2,3,4,5, \ldots, 30\}$ and ${ }^{\prime} \sim$ ' be an equivalence relation on $A \times A$, defined by $(a, b)=(c, d)$, 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 ?

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3 3 votes

Easy Way to solve this question!!

Base set is AXA Equivalence relation (a,b)=(c,d) iff ad=bc (Given)

Now ad=bc can be rewritten as a:b=c:d means ratio of both the ordered pairs has to be same.

Since ordered pair is (4,3), all equivalence ordered pairs must have ratio 4:3

Here what i did is i multiplied with 2,3,4,5,6,7 both numerator and denominator to get valid pairs.

So finally |(4,3)|={(4,3),(8,6),(12,9),(16,12),(20,15),(24,18),(28,21)} Answer:7

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