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: 95


$n(A\cup B)=27$

Work Step by Step

$A$ contains $8$ letter and $9$ numbers, for a total of $8+9=17$ elements. $B$ contains $7$ letters and $10$ numbers, for a total of $7+10=17$ elements. $A\cap B$ contains $4$ letters and $3$ numbers for a total of $4+3=7$ elements. The formula for the cardinal number of the union of two sets is the same regardless of whether certain elements are numbers or letters or something else entirely. The formula is: $n(A\cup B)=n(A)+n(B)-n(A\cap B)=17+17-7=27$
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