Question

R is a relation from [11, 12, 13] to [8, 10, 12] defined by y = x − 3. Then, R⁻¹ is

(a) [(8, 11), (10, 13)]
(b) [(11, 8), (13, 10)]
(c) [(10, 13), (8, 11), (12, 10)]
(d) none of these

Answer 1

(a) [(8, 11), (10, 13)]

R is a relation from [11, 12, 13] to [8, 10, 12], defined by y = x − 3
Now, we have:
11$-$ 3 = 8
13 $-$ 3 = 10
So, R = {(13,10),(11,8)}
∴ R⁻¹ = {(10,13),(8,11)}