let 'R' be the relation on the set N of natural numbers defined by R = {(a,b):a,b is an element of N , a+3b=12}

Find : (1) R

(2) the domain of R

(3) the range of R

R = {a, b) : a, b ∈ N, a + 3b = 12}

a + 3b = 12 ⇒ 12 – 3b

Thus, R = {(9, 1), (6, 2), (3, 3)}

We know that for a relation R from a set A to a set B, the set of all first components or coordinates of the ordered pairs belonging to R is called the domain of R, while the set of all sound components or coordinates of the ordered pairs in R is called the range of R.

∴ Domain (R) = {3, 6, 9}

Range (R) = {1, 4, 3]