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 6.3 - Page 372: 16

Answer

$For\,\,all\,\,sets\,\,A,\,B,\,\,and\,C\,\,\\ if\,\,A \cap B = \varnothing\,\,then\,\,A \times B = \varnothing.\\ this\,\,is\,\,\,false\\ counter\,\,example\,\,:\\ A=\left \{ 7 \right \},B=\left \{ 8 \right \}\\ A\cap B=\left \{ 7 \right \}\cap \left \{ 8 \right \}=\varnothing \\ But\,\,A \times B=\left \{ \left ( 7,8 \right ) \right \}\neq \varnothing $

Work Step by Step

$For\,\,all\,\,sets\,\,A,\,B,\,\,and\,C\,\,\\ if\,\,A \cap B = \varnothing\,\,then\,\,A \times B = \varnothing.\\ this\,\,is\,\,\,false\\ counter\,\,example\,\,:\\ A=\left \{ 7 \right \},B=\left \{ 8 \right \}\\ A\cap B=\left \{ 7 \right \}\cap \left \{ 8 \right \}=\varnothing \\ But\,\,A \times B=\left \{ \left ( 7,8 \right ) \right \}\neq \varnothing $
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