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: 12

Answer

$a-(4,0)\\ b-(0,1)\\ c-(2,4)\\ d-(3,3)\\$

Work Step by Step

$G: J_{5} \times J_{5}\rightarrow J_{5} \times J_{5}\\ \,For\,all\,ordered\,pairs\,(a, b)\,\in J_{5}\times J_{5} \\ G(a, b) = ((2a + 1)\,mod\,5, (3b-2)\,mod\,5) \\ a-\\ G(4, 4) = ((2(4) + 1)\,mod\,5, (3(4)-2)\,mod\,5)\\=(9\,mod\,5,10\,mod\,5)=(4,0) \\ b-\\ G(2, 1) = ((2(2) + 1)\,mod\,5, (3(1)-2)\,mod\,5)\\=(5\,mod\,5,1\,mod\,5)=(0,1) \\ c-\\ G(3, 2) = ((2(3) + 1)\,mod\,5, (3(2)-2)\,mod\,5)\\=(7\,mod\,5,4\,mod\,5)=(2,4) \\ d-\\ G(1, 5) = ((2(1) + 1)\,mod\,5, (3(5)-2)\,mod\,5)\\=(3\,mod\,5,13\,mod\,5)=(3,3) \\$
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