Let R = {(x, y) : x + 2y = 8} be a relation on ℕ, then the domain of R is:

Question

Question

Answer 1

Concept:

The domain of a relation R = {(x, y)} is the set of all values of x, and the range of R is the set of all values of y.

Calculation:

Since R is a relation on ℕ, the elements x and y must be positive integers.

We have x + 2y = 8.

⇒ y = \(\rm \dfrac{8-x}{2}= 4-\dfrac{x}{2}\).

For y to be positive and an integer (y ∈ N), we conclude that x must be divisible by 2 and \(\rm 4-\dfrac{x}{2}\) > 0.

⇒ \(\rm 4>\dfrac{x}{2}\)

⇒ x < 8.

The only numbers less than 8 which are divisible by 2 are 2, 4 and 6.

∴ x ∈ {2, 4, 6} which is the required domain.