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: 108

Answer

$n(A\cap B)[n(A\cup B)-n(A')]=2$

Work Step by Step

$n(A\cap B)$ is the number of elements of $A$ that are also elements of $B$. We can see that $n(A\cap B)=2$ $n(A\cup B)$ 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') is the number of elements in the diagram that are not in $A$. We can see that $n(A')=6$ Therefore: $n(A\cap B)[n(A\cup B)-n(A')]=2*(7-6)=2$
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