Discrete Mathematics with Applications 4th Edition

Published by Cengage Learning
ISBN 10: 0-49539-132-8
ISBN 13: 978-0-49539-132-6

Chapter 6 - Set Theory - Exercise Set 6.1 - Page 351: 32

Answer

$a-\,\,p(A\times B)=\left \{ \varnothing ,\left \{ (1,u) \right \},\left \{ (1,v) \right \},\left \{ (1,u),(1,v) \right \} \right \}$ $b-\,\,\,$ $p(X\times Y)=\left \{ \varnothing ,\left \{ (a,x) \right \},\left \{ (a,y) \right \},\left \{ (b,x) \right \},\left \{ (b,y) \right \},\left \{ (a,x),(a,y) \right \},\left \{ (a,x),(b,x) \right \},\left \{ (a,x),(b,y) \right \},\left \{ (a,y),(b,x) \right \},\left \{ (a,y),(b,y) \right \},\left \{ (b,x),(b,y) \right \},\left \{(a,x),(b,x),(a,y) \right \},\left \{ (a,x),(b,x),(b,y) \right \},\left \{ (a,x),(a,y),(b,y) \right \},\left \{ (b,x),(a,y),(b,y) \right \},\left \{ (a,x),(b,x),(a,y),(b,y) \right \} \right \}$

Work Step by Step

$a.\,\,$ $A=\left \{ 1 \right \},B=\left \{ u,v \right \}$ $A\times B=\left \{ (1,u),(1,v) \right \} $ $p(A\times B)=\left \{ \varnothing ,\left \{ (1,u) \right \},\left \{ (1,v) \right \},\left \{ (1,u),(1,v) \right \} \right \}$ $b.\,\,\,$ $X=\left \{ a,b \right \},Y=\left \{ x,y \right \} $ $X\times Y=\left \{ (a,x),(a,y),(b,x),(b,y) \right \}$ $p(X\times Y)=\left \{ \varnothing ,\left \{ (a,x) \right \},\left \{ (a,y) \right \},\left \{ (b,x) \right \},\left \{ (b,y) \right \},\left \{ (a,x),(a,y) \right \},\left \{ (a,x),(b,x) \right \},\left \{ (a,x),(b,y) \right \},\left \{ (a,y),(b,x) \right \},\left \{ (a,y),(b,y) \right \},\left \{ (b,x),(b,y) \right \},\left \{(a,x),(b,x),(a,y) \right \},\left \{ (a,x),(b,x),(b,y) \right \},\left \{ (a,x),(a,y),(b,y) \right \},\left \{ (b,x),(a,y),(b,y) \right \},\left \{ (a,x),(b,x),(a,y),(b,y) \right \} \right \}$
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