Thinking Mathematically (6th Edition)

Published by Pearson
ISBN 10: 0321867327
ISBN 13: 978-0-32186-732-2

Chapter 2 - Set Theory - 2.3 Venn Diagrams and Set Operations - Exercise Set 2.3 - Page 82: 107


$n(U)[n(A\cup B)-n(A\cap B)]=12*(7-2)=60$

Work Step by Step

$n(A\cup B)$ is the number of distinct elements which are in $A$, in $B$, or in both $A$ and $B$. We can see that $n(A\cup B)=7$ $n(A\cap B)$ is the number of elements of $A$ that are also elements of $B$. We can see that $n(A\cap B)=2$ $n(U)$ is the number of all elements in the diagram. We can see that $n(U)=12$ Therefore: $n(U)[n(A\cup B)-n(A\cap B)]=12*(7-2)=60$
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