Discrete Mathematics and Its Applications, Seventh Edition

Published by McGraw-Hill Education
ISBN 10: 0073383090
ISBN 13: 978-0-07338-309-5

Chapter 2 - Section 2.3 - Functions - Exercises - Page 153: 19

Answer

a) All the offices the school. b) The set of buses going on a field trip. c) all positive real numbers ( each representing the salary in dollars). d) All strings of nine digits.

Work Step by Step

a) All the offices the school. This is not onto as there will be offices not assigned to any of the teachers. If we change the codomian to to "all offices occupied by at least one teacher", it becomes onto. b) The set of buses going on a field trip. If every bus has to have a teacher chaperone , this is an onto function. c) all positive real numbers ( each representing the salary in dollars). The function is not onto as no teacher has a salary of $\pi$ dollars. It can be onto if codomain contains only the actual salaries of the teachers. d) All strings of nine digits. This function is not onto, as there will be a string assigned to a person not teaching at the school. For the function to be onto, the codomain will contain only the teachers of social security number.
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