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:
A = (3, 5) and B = (7, 11)
Also,
R = {(a, b) : a ∈ A, b ∈ B, a − b is odd}
a are the elements of A and b are the elements of B.

$$\begin{gathered} \therefore a-b=3-7,3-11,5-7,5-11 \\ \Rightarrow a-b=-4,-8,-2,-6 \\ \mathrm{Here},a-b\mathrm{is}\mathrm{always}\mathrm{an}\mathrm{even}\mathrm{number}. \end{gathered}$$
So, R is an empty relation from A to B.
Hence proved.