Let A = {3, 5} and B = {7, 11}. Let R = {(a, b): a A, b B, a-b is odd}. Show that R is an empty relation from into B.
Given, A = {3, 5} and B = {7, 11}
R = {(a, b): a A, b B, a-b is odd}
On putting a = 3 and b = 7:
⇒ a – b = 3 – 7 = -4 which is not odd
On putting a = 3 and b = 11:
⇒ a – b = 3 – 11 = -8 which is not odd
On putting a = 5 and b = 7:
⇒ a – b = 5 – 7 = -2 which is not odd
On putting a = 5 and b = 11:
⇒ a – b = 5 – 11 = -6 which is not odd
∴ R = { } = Φ
⇒ R is an empty relation from into B