GATE | GATE MOCK 2017 | Question 13

Let A = {a, b, c, d }, B = { p, q, r, s } denote sets.
R : A –> B, R is a function from A to B. Then which of the following relations are not functions ?
(i) { (a, p) (b, q) (c, r) }

(ii) { (a, p) (b, q) (c, s) (d, r) }
(iii) { (a, p) (b, s) (b, r) (c, q) }

(A) (i) and (ii) only

(B) (ii) and (iii) only

(C) (i) and (iii) only
(D) None of these

Answer: (C)

Explanation: (i) is not a function since the element d (∈A) is not related to any element in B.
(iii) is not a function since b (∈A) is associated with two different elements of B.

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