Let A = {2, 3, 4, 5, ldots, 30} and simeq be | vedclass

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(D) Given the set $A = \{2, 3, 4, 5, \ldots, 30\}$.The equivalence relation is defined as $(a, b) \simeq (c, d)$ if and only if $ad = bc$.We need to f

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$7$

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(D) Given the set $A = \{2, 3, 4, 5, \ldots, 30\}$.The equivalence relation is defined as $(a, b) \simeq (c, d)$ if and only if $ad = bc$.We need to find the number of ordered pairs $(c, d)$ such that $(c, d) \simeq (4, 3)$.Using the definition,we have $c 	imes 3 = d 	imes 4$,which implies $\frac{c}{d} = \frac{4}{3}$.This means $c = 4k$ and $d = 3k$ for some constant $k$,where $c, d \in A$.Since $c, d \in \{2, 3, \ldots, 30\}$,we check the possible values for $k$:For $k=1: (c, d) = (4, 3)$For $k=2: (c, d) = (8, 6)$For $k=3: (c, d) = (12, 9)$For $k=4: (c, d) = (16, 12)$For $k=5: (c, d) = (20, 15)$For $k=6: (c, d) = (24, 18)$For $k=7: (c, d) = (28, 21)$For $k=8: (c, d) = (32, 24)$,which is not possible since $32 
otin A$.Thus,the possible ordered pairs are $(4, 3), (8, 6), (12, 9), (16, 12), (20, 15), (24, 18), (28, 21)$.The total number of such ordered pairs is $7$.

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 $(c, d)$ which satisfy this equivalence relation with the ordered pair $(4, 3)$ is equal to:

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