# Let A = [p, q, r, s] and B = [1, 2, 3].

Question:

Let A = [pqrs] and B = [1, 2, 3]. Which of the following relations from A to B is not a function?

(a) R1 = [(p, 1), (q, 2), (r, 1), (s, 2)]

(b) R2 = [(p, 1), (q, 1), (r, 1), (s, 1)]

(c) R3 = [(p, 1), (q, 2), (p, 2), (s, 3)

(d) R4 = [(p, 2), (q, 3), (r, 2), (s, 2)].

Solution:

(c) R3 = [(p, 1), (q, 2), (p, 2), (s, 3)

All the relations in (a), (b) and (d) have a unique image in B for all the elements in A.

R3 is not a function from A to B because ∈ A has two images, 1 and 2, in B.

Hence, option (c) is not a function.