Let A = (3, 5) and B = (7, 11).
Question:

Let A = (3, 5) and B = (7, 11). Let R = {(ab) : a ∈ A, b ∈ B, a − b is odd}. Show that R is an empty relation from A into B.

Solution:

Given:

A = (3, 5) and B = (7, 11)

Also,

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

a are the elements of A and b are the elements of B.

$\therefore a-b=3-7,3-11,5-7,5-11$

$\Rightarrow a-b=-4,-8,-2,-6$

Here, $a-b$ is always an even number.

So, R is an empty relation from A to B.

Hence proved.