Question

Let A = {6, 8} and B = {1, 3, 5}.
Let R = {(a, b)/a∈ A, b∈ B, a – b is an even number}. Show that R is an empty relation from A to B.

Answer 1

A = {6, 8} and B = {1, 3, 5}
R = {(a, b)/a ∈ A, b ∈ B, a - b is an even number}
a ∈ A
∴ a = 6, 8
b ∈ B
∴ b = 1, 3, 5
When a = 6 and b = 1, a - b = 5 which is odd
When a = 6 and b = 3, a - b = 3 which is odd
When a = 6 and b = 5, a - b = 1 which is odd
When a = 8 and b = 1, a - b = 7 which is odd
When a = 8 and b = 3, a - b = 5 which is odd
When a = 8 and b = 5, a - b = 3 which is odd
Thus, no set of values of a and b gives a - b even
∴ R is an empty relation from A to B.