Basic College Mathematics (9th Edition)

Published by Pearson
ISBN 10: 0321825535
ISBN 13: 978-0-32182-553-7

Appendix: Inductive and Deductive Reasoning - Appendix Exercises: 19

Answer

Neither the husband nor the wife watched television in $3$ of the $30$-day period. Refer to the Venn Diagram below,
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Work Step by Step

Draw two circles that overlap and label them (Husband, Wife). The husband and wife watched television together for 18 days so write $18$ in the region where the circles overlap. Since the husband watched television for a total of $20$ days, then it means that in $20-18=2$ of those days, he watched all by himself. Since the wife watched television for a total of $25$ days, then it means that in $25-18=7$ of those days, she watched all by herself, Write $2$ in the non-overlapping region inside the circle for Husband. Write $7$ in the non-overlapping region inside the circle for Wife. The two circles contain 18, 2, and 7. Thus, either of them watched television for a total of $18+2+7=27$ days. Therefore, in the given 30-day period, neither the husband nor the wife watched television for $30-17=3$ days.
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