Given, (x, y) R x + 2y = 8 where x N and y N

x = 8 – 2y

As y N, Put the values of y = 1, 2, 3,…… till x N

On putting y=1, x = 8 – 2(1) = 8 – 2 = 6

On putting y=2, x = 8 – 2(2) = 8 – 4 = 4

On putting y=3, x = 8 – 2(3) = 8 – 6 = 2

On putting y=4, x = 8 – 2(4) = 8 – 8 = 0

Now, y cannot hold value 4 because x = 0 for y = 4 which is not a natural number.

∴ R = {(2, 3), (4, 2), (6, 1)}

An inverse relation is the set of ordered pairs obtained by interchanging the first and second elements of each pair in the original relation. If the graph of a function contains a point (a, b), then the graph of the inverse relation of this function contains the point (b, a).

R^‑1 = {(3, 2), (2, 4), (1, 6)}

⇒R^‑1 = {(1, 6), (2, 4), (3, 2)}