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 7.2 - Page 415: 27

Answer

T: Z+ → D T (n) = the set of all of the positive divisors of n. a) one to one: True Proof : let's assume that p and q have the same image such that T(p) = T(q) T(p) and T(q) sets have the largest integer divisor let it be X, now since they have the same image that means they have the same X and the largest divisor of a positive integer is the integer itself hence p= q = X. b) onto : False, counterexample {1,2,3} $\in$ D but there is no positive integer with {1,2,3} as its divisor since 3 is a prime and 6 Is missing itself from the set.

Work Step by Step

T: Z+ → D T (n) = the set of all of the positive divisors of n. a) one to one: True Proof : let's assume that p and q have the same image such that T(p) = T(q) T(p) and T(q) sets have the largest integer divisor let it be X, now since they have the same image that means they have the same X and the largest divisor of a positive integer is the integer itself hence p= q = X. b) onto : False, counterexample {1,2,3} $\in$ D but there is no positive integer with {1,2,3} as its divisor since 3 is a prime and 6 Is missing itself from the set.
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