Let A = {2, 3, 4, 5, …, 17, 18}. Let ‘ ≃ ’ be the equivalence relation on A × A, cartesian product of A with itself, defined by (a, b) ≃ (c, d) iff ad = bc. Then, the number of ordered pairs of the equivalence class of (3, 2) is

Question

Philoid · Accepted Answer

Let (3,2) ≃ (x,y)

⇒ 3y = 2x

This is possible in the cases:

x = 3, y = 2

x = 6, y = 4

x= 9, y =6

x=12, y = 3

x=15, y = 10

x=18,y=12

Hence total pairs are 6.

Let A = {2, 3, 4, 5, …, 17, 18}. Let ‘≃’ be the equivalence relation on A × A, cartesian product of A with itself, defined by (a, b) ≃ (c, d) iff ad = bc. Then, the number of ordered pairs of the equivalence class of (3, 2) is