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 350: 19

Answer

a- $\left \{ 1,2,3,4,9,16 \right \}$ b-$\varnothing$ c- $A_{1}, A_{2}, A_{3}\, and\, A_{4}$ are not mutually disjoint

Work Step by Step

$A_{i}=\left \{ i,i^{2} \right \}\,\,for\,\, i=1,2,3,4$$A_{1}= \left \{ 1,1 \right \},A_{2}=\left \{ 2,4 \right \},A_{3}=\left \{ 3,9 \right \},A_{4}=\left \{ 4,16 \right \}$ $a.\,\, \,A_{1}\cup A_{2}\cup A_{3}\cup A_{4}=\left \{ 1,1 \right \}\cup \left \{ 2,4 \right \}\cup \left \{ 3,9 \right \}\cup \left \{ 4,16 \right \}=\left \{ 1,2,3,4,9,16 \right \}$ $b. \,\, A_{1}\cap A_{2}\cap A_{3}\cap A_{4}= \left \{ 1,1 \right \}\cap \left \{ 2,4 \right \}\cap \left \{ 3,9 \right \}\cap \left \{ 4,16 \right \}= \varnothing $ $c.\,\, A_{1},A_{2},A_{3}\,and A_{4}\,\, are\,not\,mutually\,\, disjoint \, because \,\, \, A_{2}\,, A_{4}\, \,both\,\, contain \,\,4\,\, A_{2}\cap A_{4}=\left \{ 2,4 \right \}\cap \left \{ 4,16 \right \}=\left \{ 4 \right \}\neq \varnothing $
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