1. Copyright © 2009 Pearson Education, Inc. Chapter 2 Section 5 - Slide 1 Section 5 Applications of Sets

2. Chapter 2 Section 5 - Slide 2 Copyright © 2009 Pearson Education, Inc. Example: Toothpaste Taste Test A drug company is considering manufacturing a new toothpaste. They are considering two flavors, regular and mint. In a sample of 120 people, it was found that 74 liked the regular, 62 liked the mint, and 35 liked both types. How many liked only the regular flavor? How many liked either one or the other or both? How many people did not like either flavor?

3. Chapter 2 Section 5 - Slide 3 Copyright © 2009 Pearson Education, Inc. Solution Begin by setting up a Venn diagram with sets A (regular flavor) and B (mint flavor). Since some people liked both flavors, the sets will overlap and the number who liked both with be placed in region II. 35 people liked both flavors. U A(Regular) B(Mint) 35 II

4. Chapter 2 Section 5 - Slide 4 Copyright © 2009 Pearson Education, Inc. Solution (continued) Next, region I will refer to those who liked only the regular and region III will refer to those who liked only the mint. In order to get the number of people in each region, find the difference between all the people who liked each toothpaste and those who liked both. I: 74 – 35 = 39 III: 62 – 35 = 27 U A(Regular) B(Mint) 39 regular only 27 mint only III II I both 35

5. Chapter 2 Section 5 - Slide 5 Copyright © 2009 Pearson Education, Inc. Solution (continued) “One or the other or both” represents the UNION of the two sets. Therefore, 39 + 27 + 35 = 101 people who liked one or the other or both.

6. Chapter 2 Section 5 - Slide 6 Copyright © 2009 Pearson Education, Inc. Solution (continued) Take the total number of people in the entire sample and subtract the number who liked one or the other or both. 120-101 = 19 people did not like either flavor. U A(Regular) B(Mint) 35 both 62-35=27 Likedmint only 74-35=39 Likedregular only 19 liked neither I I I I I

7. Chapter 2 Section 5 - Slide 7 Copyright © 2009 Pearson Education, Inc. Example: Ice Cream Flavors The Ice Cream Shoppe surveyed its customers about their preferences of three ice cream flavors. The results of the survey showed the following number of people liked the respective flavor(s): vanilla170 vanilla & chocolate100 chocolate135 vanilla & strawberry74 strawberry103 chocolate & strawberry52 all three35 none of the three7

8. Chapter 2 Section 5 - Slide 8 Copyright © 2009 Pearson Education, Inc. Using a Venn diagram, determine how many people completed the survey.

9. Chapter 2 Section 5 - Slide 9 Copyright © 2009 Pearson Education, Inc. Solution 31 65 35 39 18 17 +12 217