Let $A = \{2, 3, 4, 5, \ldots, 16, 17, 18\}$. Let $R$ be the relation on the set $A$ of ordered pairs of positive integers defined by $(a, b) R (c, d)$ if and only if $ad = bc$ for all $(a, b), (c, d) \in A imes A$. 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 $R$ be the relation on the set $A$ of ordered pairs of positive integers defined by $(a, b) R (c, d)$ if and only if $ad = bc$ for all $(a, b), (c, d) \in A 	imes A$. Then the number of ordered pairs of the equivalence class of $(3, 2)$ is:

cdquestions Admin · Accepted Answer

The equivalence relation $(a, b) R (c, d)$ is defined by $ad = bc$. For $(3, 2)$, the equivalence class consists of all $(c, d)$ such that: $$ 3d = 2c. $$ Since $c, d \in \{2, 3, 4, \ldots, 18\}$, solving for integer pairs $(c, d)$ satisfying $3d = 2c$ gives six solutions.

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Answer

Let $A = \{2, 3, 4, 5, \ldots, 16, 17, 18\}$. Let $R$ be the relation on the set $A$ of ordered pairs of positive integers defined by $(a, b) R (c, d)$ if and only if $ad = bc$ for all $(a, b), (c, d) \in A \times A$. Then the number of ordered pairs of the equivalence class of $(3, 2)$ is:

The Correct Option is C

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