Discrete Mathematics with Applications 4th Edition

Published by Cengage Learning
ISBN 10: 0-49539-132-8
ISBN 13: 978-0-49539-132-6

Chapter 7 - Functions - Exercise Set 7.1 - Page 394: 3

Answer

a. True. b. False. c. True. d. False.

Work Step by Step

The definition of a function is used in each part. A function f: X → Y satisfies 2 properties: 1. Every element in X is related to an element in Y. 2. No single x∈X is related to more than one y∈Y. a. By the second property, since each element in X relates to only 1 element in Y then if both elements are the same in X then they must relate to the same element in Y. b. The properties of a function do not stop 2 different elements in X from relating to the same element in Y. That is, 2 different elements e.g. a, b ∈ X can point to the same y∈Y. So if 2 elements in Y are the same it does not guarantee that the elements in X that are related to those 2 elements in Y are equal as well. c. This is true for the same reason that the previous question (b) is false. The properties of a function do not prohibit 2 different elements in X from pointing to the same element in Y. d. This is false because it violates property (2) which is that no element in X can point to more than one element in Y. **Note relate and point mean the same thing in this context.
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