Question

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 A into B.

Answer 1

Given as

A = {3, 5} and B = {7, 11}

R = {(a, b): a ∈ A, b ∈ B, a-b is odd}

Putting a = 3 and b = 7,

a – b = 3 – 7 = -4 which is not odd

Putting a = 3 and b = 11,

a – b = 3 – 11 = -8 which is not odd

Putting a = 5 and b = 7:

a – b = 5 – 7 = -2 which is not odd

Putting a = 5 and b = 11:

a – b = 5 – 11 = -6 which is not odd

∴ R = { } = Φ

R is an empty relation from A into B.

Thus proved.