Let
Question:

Let $A=\{2,3,4,5, \ldots, 17,18\}$. Let ‘ $\simeq$ ‘ be the equivalence relation on $A \times A$, cartesian product of $A$ with itself, defined by ( $a, b$ ) $\simeq$ $(c, d)$ if $a d=b c$. Then, the number of ordered pairs of the equivalence class of $(3,2)$ is

(a) 4
(b) 5
(c) 6
(d) 7

Solution:

(c) 6

The ordered pairs of the equivalence class of (3, 2) are {(3, 2), (6, 4), (9, 6), (12, 8), (15, 10), (18, 12)}.
We observe that these are 6 pairs.

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