Let `A={2,\ 3,\ 4,\ 5,\ .......\ 17 ,\ 18}` . Let `' '` be the equivalence relation on `AxxA` , cartesian product of `A` with itself, defined by `(a ,\ b)(c ,\ d)` iff `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

Options

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

Answer

C

Explanation

The number of ordered pairs in the equivelence class of (3,2) is the number of ordered pairs (a,b) satisfying
`(a,b) ~=(3,2)i.e. 2a=3b i.e. (a)/(b) =(3)/(2)`
Clearly, such ordered pairs are
(3,2), (6,4), (9,6), (12,8), (15,10) and (18,12).