(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 Relation and Function 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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Consider the relations $R_1$ and $R_2$ defined as $a R_1 b \Leftrightarrow a^2+b^2=1$ for all $a, b \in R$ and $(a, b) R_2 (c, d) \Leftrightarrow a+d=b+c$ for all $(a, b), (c, d) \in N \times N$. Then:

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Let $R$ be a relation from $N$ to $N$ defined by $R = \{(a, b) : a, b \in N \text{ and } a = b^2\}$. Is the following statement true?
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Let $T$ be the set of all triangles in a plane with $R$ a relation in $T$ given by $R = \{(T_1, T_2) : T_1 \text{ is congruent to } T_2\}$. Show that $R$ is an equivalence relation.

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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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Consider the relations $R_1$ and $R_2$ defined as $a R_1 b \Leftrightarrow a^2+b^2=1$ for all $a, b \in R$ and $(a, b) R_2 (c, d) \Leftrightarrow a+d=b+c$ for all $(a, b), (c, d) \in N \times N$. Then:

Let $S$ be the set of all real numbers. Then the relation $R = \{(a, b) : 1 + ab > 0\}$ on $S$ is

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Let $R$ be a relation from $N$ to $N$ defined by $R = \{(a, b) : a, b \in N \text{ and } a = b^2\}$. Is the following statement true?$(a, b) \in R, (b, c) \in R$ implies $(a, c) \in R$

Let $T$ be the set of all triangles in a plane with $R$ a relation in $T$ given by $R = \{(T_1, T_2) : T_1 \text{ is congruent to } T_2\}$. Show that $R$ is an equivalence relation.

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Let $R$ be a relation from $N$ to $N$ defined by $R = \{(a, b) : a, b \in N \text{ and } a = b^2\}$. Is the following statement true?
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