Question

Let A = {3, 4} and B = {7, 9}. Let R = {(a, b): a ϵ A, b ϵ B and (a – b) is odd}. Show that R is an empty relation from A to B.

Answer 1

Given: A = {3, 4} and B = {7, 9} 

R = {(a, b): a ϵ A, b ϵ B and (a – b) is odd} 

So, R = {(4, 7), (4, 9)} 

An empty relation means there is no elements in the relation set. 

Here we get two relations which satisfy the given conditions. 

Therefore, the given relation is not an Empty Relation. 

The given relation would be an Empty Relation if, 

(1) A = {3} or, 

(2) A = {3, any odd number} or,