Let `R` be a relation in `N` defined by `(x ,y) in R x+2y=8` . Express `Ra n dR^(-1)` as sets of ordered pairs.

Explanation

Given as `(x, y) inR x + 2y = 8 `where x ∈ N and y ∈ N

`x + 2y= 8 x = 8 – 2y`

By putting the values `y = 1, 2, 3,…… till x ∈ N `

If, `y = 1, x = 8 – 2(1) = 8 – 2 = 6`
If,` y = 2, x = 8 – 2(2) = 8 – 4 = 4 `
If, `y = 3, x = 8 – 2(3) = 8 – 6 = 2`
If, `y = 4, x = 8 – 2(4) = 8 – 8 = 0 `
Then, y cannot hold value 4 because `x = 0 `for` y = 4 `which is not a natural number.

∴` R = {(2, 3), (4, 2), (6, 1)} `
Thus,` R^(-1) = {(3, 2), (2, 4), (1, 6)} `