Let $A = \{ 2,\ 3,\ 4,\ 5,\ \ldots,\ 16,\ 17,\ 18\}$. Let be the equivalence relation on $A imes A$, cartesian product of $A$ and $A$, defined by $(a,\ b) \approx (c,\ d)$ if $ad = bc$, then the number of ordered pairs of the equivalence class of (3, 2) is

Question

Let $A = \{ 2,\ 3,\ 4,\ 5,\ \ldots,\ 16,\ 17,\ 18\}$. Let be the equivalence relation on $A 	imes A$, cartesian product of $A$ and $A$, defined by $(a,\ b) \approx (c,\ d)$ if $ad = bc$, then the number of ordered pairs of the equivalence class of (3, 2) is

Dr. Abubacker · Accepted Answer

(c)
Given, $A = \{ 2,\ 3,\ 4,\ 5,\ldots.,16,\ 17,\ 18\}$
And $(a,\ b) = (c,\ d)$
$	herefore$ Equivalence class of $(3,\ 2)$ is
$\ \ \ \ \{(a,\ b) \in A 	imes A:(a,\ b)R\ (3,\ 2)\}$
$\ \ \ \ \  = \left\{ (a,\ b) \in A 	imes A:2a = 3b ight\}$
$\ \ \ \  = \left\{ (a,\ b) \in A 	imes A:b = \frac{2}{3}a ight\}$
$\ \ \ \ \ \left\{ \left( a,\ \frac{2}{3}a ight):a \in A 	imes A ight\}$
$\ \ \  = \{(3,\ 2),\ (6,\ 4),\ (9,\ 6),\ (12,\ 8),\ (15,\ 10),\ (18,\ 12)\}$
$	herefore$ Number of ordered pairs of the equivalence class=6.

Q. Let $A = \{ 2,\ 3,\ 4,\ 5,\ \ldots,\ 16,\ 17,\ 18\}$. Let be the equivalence relation on $A \times A$, cartesian product of $A$ and $A$, defined by $(a,\ b) \approx (c,\ d)$ if $ad = bc$, then the number of ordered pairs of the equivalence class of (3, 2) is

Explanation

Reviewed by Dr. Abubacker

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