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 395: 25

Answer

$a-\,\,p_{1}(2, y) = 2\,\,\,,\,\,p_{1}(5, x) = 5 \\ Range\,of\,p_{1}=\left \{ 2,3,5 \right \}=A\\ b- \\ p_{2}(2,y)=y\,\,\,\,,p_{2}(5,x)=x\\ Range\,of\,p_{2}=\left \{ x,y \right \}=B\\$

Work Step by Step

$ for\,\,each\,\,pair\,\,(a, b)\in A \times B \\ p_{1}(a, b) = a\,\,,and\,\,\,p_{2}(a, b) = b.\\ A=\left \{ 2,3,5 \right \},B=\left \{ x,y \right \}\\ a-\,\,p_{1}(2, y) = 2\,\,\,,\,\,p_{1}(5, x) = 5 \\ A\times B=\left \{ (2,x),(2,y),(3,x),(3,y),(5,x),(5,y) \right \}\\ p_{1}(2,x)=2 \,\,\,\,,p_{1}(2,y)=2 \\ p_{1}(3,x)=3 \,\,\,\,,p_{1}(3,y)=3 \\ p_{1}(5,x)=5 \,\,\,\,,p_{1}(5,y)=5 \\ Range\,of\,p_{1}=\left \{ 2,3,5 \right \}=A\\ b-p_{2}(2,y)=y\,\,\,\,,p_{2}(5,x)=x\\ p_{2}(2,x)=x \,\,\,\,,p_{2}(2,y)=y \\ p_{2}(3,x)=x \,\,\,\,,p_{2}(3,y)=y \\ p_{2}(5,x)=x \,\,\,\,,p_{2}(5,y)=y \\ Range\,of\,p_{2}=\left \{ x,y \right \}=B\\ $
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