EX. NO. 1.3, RELATIONS AND FUNCTIONS, 10TH MATHS NEW SYLLABUS, TAMIL NADU, TN, 1. Let f = {(x, y) | x, y ∈ N and y = 2x} be a relation on ℕ. Find the domain, co-domain and range. Is this relation a function? Solution : Since x and y ∈ N, x = 1 y = 2(1) y = 2 x = 2 y = 2(2) y = 4 x = 3 y = 2(3) y = 6 x = 4 y = 2(4) y = 8 f = {(1, 2) (2, 4) (3, 6) (4, 8)................} For each values of x, we get different values of y. So the given relation is a function. Domain is the set of values of x Domain = {1, 2, 3, 4, ............} Co domain is the set of value of y. Since y ∈ N Co domain = {1, 2, 3, 4, .............} Range means the set of values of y, which are associated with x. Range = {2, 4, 6, 8, .....} 2. Let X = {3, 4, 6, 8}. Determine whether the relation ℝ = {(x, f (x)) | x ∈ X, f (x) = x 2 + 1} is a function from X to ℕ ? Solution : Given that : f (x) = x 2 + 1 x ∈ X if x = 3 f(3) = 3 2 +1 f(