Let A -p- q- r- s- and B -1-2-3- Which of the following relations from A to B is not a function-a R 1-p- 1-q- 2-r- 1-s- 2-b R 2-p- 1-q- 1-r- 1-s- 1-c R 3-p- 1-q- 2-p- 2-s- 3d R 4-p- 2-q- 3-r- 2-s- 2-

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Mathematics

Onto Function

Let A =[p, q,...

Question

Let A = [p, q, r, s] 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)].

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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 p ∈ A has two images, 1 and 2, in B.
Hence, option (c) is not a function.

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Let A = [p, q, r, s] 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)].

(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 p ∈ A has two images, 1 and 2, in B. Hence, option (c) is not a function.

Let A = [p, q, r, s] 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)].

(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 p ∈ A has two images, 1 and 2, in B.
Hence, option (c) is not a function.