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: 10

Answer

$ a-T(1)=\left \{ 1 \right \}\\ b-T(15)=\left \{ 1,3,5,15 \right \}\\ c-T(17)=\left \{ 1,17 \right \}\\ d-T(5)=\left \{ 1,5 \right \}\\ e-T(18)=\left \{ 1,2,3,6,9,18 \right \}\\ f-T(21)=\left \{ 1,3,7,21 \right \}\\ $

Work Step by Step

$T:Z^+\rightarrow D \\ T(n)=\,the\,set\,of\,positive\,divisors\,of\,\,n.\\ divisors\,of\,\,1 :1\\ T(1)=\left \{ 1 \right \}\\ divisors\,of\,\,15:1,3,5,15 \\ T(15)=\left \{ 1,3,5,15 \right \}\\ divisors\,of\,\,17:1,17\\ T(17)=\left \{ 1,17 \right \}\\ divisors\,of\,\,5:1,5\\ T(5)=\left \{ 1,5 \right \}\\ divisors\,of\,\,18:1,2,3,6,9,18\\ T(18)=\left \{ 1,2,3,6,9,18 \right \}\\ divisors\,of\,\,21:1,3,7,21\\ T(21)=\left \{ 1,3,7,21 \right \}\\ $
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