Question

Find the domain and range of the relation R given by

R = {(x, y) : y =x + 6/x; where x, y ∈ N and x < 6}.

Answer 1

When x = 1, y = 7 ∈ N, so (1, 7) ∈ R. Again for,

x = 2 . y = 2 + 6/2 = 2 + 3 = 5 ∈ N, so (2, 5) ∈ R. 

Again for

x = 3, y = 3 + 6/3 = 3 + 2 = 5 ∈ N, (3, 5) ∈ R. Similarly for x = 4

y = 4 + 6/4 ∉ N and for x = 5 , y = 5 + 6/5 ∉ N

Thus R = {(1, 7), (2, 5), (3, 5)}, where Domain of R = {1, 2, 3}

Range of R = {7, 5}