(C) The equivalence class of $(3, 2)$ consists of all pairs $(x, y) \in A \times A$ such that $(x, y) R (3, 2)$.This implies $2x = 3y$,or $\frac{x}{y}

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(C) The equivalence class of $(3, 2)$ consists of all pairs $(x, y) \in A \times A$ such that $(x, y) R (3, 2)$.This implies $2x = 3y$,or $\frac{x}{y} = \frac{3}{2}$.Since $x, y \in \{2, 3, \ldots, 18\}$,we look for multiples of $(3, 2)$ such that both components are $\le 18$:$(x, y) = (3, 2)$$(x, y) = (6, 4)$$(x, y) = (9, 6)$$(x, y) = (12, 8)$$(x, y) = (15, 10)$$(x, y) = (18, 12)$Counting these,we have $6$ such ordered pairs.

Class 12 Mathematics Relations and Functions Types of Relations

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Let $A = \{2, 3, 4, 5, \ldots, 16, 17, 18\}$. Let $R$ be the relation on the set $A \times A$ 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 in the equivalence class of $(3, 2)$ is:

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A
$4$
B
$5$
C
$6$
D
$7$

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Let $A = \{2, 3, 4, 5, \ldots, 16, 17, 18\}$. Let $R$ be the relation on the set $A \times A$ 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 in the equivalence class of $(3, 2)$ is:

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The number of non-empty equivalence relations on the set $\{1, 2, 3\}$ is :

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