Functions Equivalence Mock 6

We are given the condition:

(a, b) ~ (4, 3) means ad = bc

So:

a × 3 = b × 4

⇒ 3a = 4b

Rearrange:

a = (4/3) b

For a to be an integer, b must be divisible by 3.

Now b ranges from 2 to 30. Multiples of 3 in this range are:

3, 6, 9, 12, 15, 18, 21, 24, 27, 30

Now find a for each:

b = 3 → a = 4

b = 6 → a = 8

b = 9 → a = 12

b = 12 → a = 16

b = 15 → a = 20

b = 18 → a = 24

b = 21 → a = 28

b = 24 → a = 32 (not allowed, outside set)

b = 27 → a = 36 (not allowed)

b = 30 → a = 40 (not allowed)

Since A only goes up to 30, only first 7 pairs are valid.

Answer = 7