Discrete Mathematics and Its Applications, Seventh Edition

Published by McGraw-Hill Education
ISBN 10: 0073383090
ISBN 13: 978-0-07338-309-5

Chapter 2 - Section 2.2 - Set Operations - Exercises - Page 136: 2

Answer

a) $A\cap B$ b) $A- B$, or equivalently $A \cap \overline B$ c) $A \cup B$ d) $\overline A \cup \overline B$, or equivalently $\overline {A \cap B}$

Work Step by Step

a) This is the set of students who are sophomores and who are taking discrete mathematics, so this is the set of students who are in both $A$ and $B$. Hence this set is $A\cap B$. b) This is the set of students who are sophomores and who are not taking discrete mathematics, so this is the set of students who are in $A$ but not in $B$. Hence this set is $A- B$, or equivalently $A \cap \overline B$ c) The set of students who are either sophomores or taking discrete mathematics is the set of students who are in $A$, or in $B$, or in both $A$ and $B$. So this set it $A \cup B$. d) The set of students who are not sophomores and who are not taking discrete mathematics is the set of students who are either not in $A$ (i.e., in $\overline A$) or not in $B$ (i.e., in $\overline B$). So this set is $\overline A \cup \overline B$, or equivalently $\overline {A \cap B}$.
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