Thinking Mathematically (6th Edition)

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

Chapter 2 - Set Theory - Chapter Summary, Review, and Test - Review Exercises - Page 110: 61

Answer

Venn diagram

Work Step by Step

(a) The number of students who used only public transportation is represented by region VII: \[\begin{align} & \text{Number of students who used public transportation}=n\left( \text{VII} \right) \\ & =50 \end{align}\] (b) The number of students who usedboth cars and public transportation but not bikes is represented by region VI: \[\begin{align} & \text{Number of students who used both cars and public transport but not bikes}=n\left( \text{VI} \right) \\ & =26 \end{align}\] (c) The number of students who used cars or public transportation but not bikes is represented by sum of the regions V, VI, and VII: \[\begin{align} & \text{Number of students who used cars or public transportation but not bikes}=n\left( \text{V} \right)+n\left( \text{VI} \right)+n\left( \text{VII} \right) \\ & =54+26+50 \\ & =130 \end{align}\] (d) The number of students who used exactly two of these modes of transportation is represented by the sum of the regions II, IV, and VI: \[\begin{align} & \text{Number of students who used exactly two modes of transportation}=n\left( \text{II} \right)+n\left( \text{IV} \right)+n\left( \text{VI} \right) \\ & =16+4+26 \\ & =46 \end{align}\] (e) The number of students who did not use any of the three modes is represented by region VIII: \[\begin{align} & \text{Number of students who did not use any of the three modes}=n\left( \text{VII} \right) \\ & =0 \end{align}\]
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