Let A = 2, 3, 4, 5, ....., 30 and '[ ]' be an equivalence relation on A [] A, defined by (…

Question

Let A = {2, 3, 4, 5, ....., 30} and '$$ \simeq $$' be an equivalence relation on A $$\times$$ A, defined by (a, b) $$ \simeq $$ (c, d), if and only if ad = bc. Then the number of ordered pairs which satisfy this equivalence relation with ordered pair (4, 3) is equal to :

Accepted Answer

ad = bc

(a, b) R (4, 3) $$ \Rightarrow $$ 3a = 4b

a = $${4 \over 3}$$b

b must be multiple of 3

b = {3, 6, 9 ..... 30}

(a, b) = {(4, 3), (8, 16), (12, 9), (16, 12), (20, 15), (24, 18), (28, 21)}

$$ \Rightarrow $$ 7 ordered pair

Solutions · 1