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: 3

Answer

$counter\,\,example\,\,:\\ A=\left \{ 1,2 \right \},B=\left \{ 4,5 \right \},C=\left \{ 1,2,3 \right \}\\ $

Work Step by Step

$For\,\,all\,\,sets\,\,A,\,B,\,and\,\,C\,\\ if\,A\nsubseteq B \,and\,B\nsubseteq C\,then\,A\nsubseteq C \\ this\,\,is\,\,not\,\,true:\\ counter\,\,example\,\,:\\ A=\left \{ 1,2 \right \},B=\left \{ 4,5 \right \},C=\left \{ 1,2,3 \right \}\\ notice\,\,that\,\,A\nsubseteq B\,\,and\,B\nsubseteq C \\ \left \{ 1,2 \right \}\nsubseteq \left \{ 4,5 \right \},\left \{ 4,5 \right \}\nsubseteq \left \{ 1,2,3 \right \}\\ but \,\, A\subseteq C \,\,\,\left \{ 1,2 \right \}\subseteq \left \{ 1,2,3 \right \} $
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