Upload
warren-lucas
View
42
Download
0
Embed Size (px)
DESCRIPTION
Section 2.5 Application of Sets. What You Will Learn. Application of Sets. Example 1: Yogurt Taste Test. - PowerPoint PPT Presentation
Citation preview
Copyright 2013, 2010, 2007, Pearson, Education, Inc.
Section 2.5
Application of Sets
Copyright 2013, 2010, 2007, Pearson, Education, Inc.
What You Will Learn
Application of Sets
2.5-2
Copyright 2013, 2010, 2007, Pearson, Education, Inc.
A yogurt company wishes to introduce a new yogurt flavor. The company is considering two flavors: raspberry cheesecake (R) and orange creme (O). In a survey of 250 people it was found that180 people liked raspberry cheesecake.139 people liked orange creme.82 people liked both flavors.
Example 1: Yogurt Taste Test
2.5-3
Copyright 2013, 2010, 2007, Pearson, Education, Inc.
Of those surveyed, how many peoplea) did not like either raspberry
cheesecake or orange crème?b) liked raspberry cheesecake, but
not orange creme?c) liked orange creme, but not
raspberry cheesecake?d) liked either raspberry
cheesecake or orange creme?
Example 1: Yogurt Taste Test
2.5-4
Copyright 2013, 2010, 2007, Pearson, Education, Inc.
SolutionPeople surveyed is 250: n(U) = 250.People surveyed who liked raspberry cheesecake is 180: n(R) = 180.
People surveyed who liked orange creme is 139: n(O) = 139.
People surveyed who liked both raspberry cheesecake and orange creme is 82: n(R ⋂ O) = 82.
Example 1: Yogurt Taste Test
2.5-5
Copyright 2013, 2010, 2007, Pearson, Education, Inc.
SolutionRegion II is n(R ⋂ O) = 82 I is n(R) – n(R ⋂ O) = 180 – 82 = 98III is n(O) – n(R ⋂ O) = 139 – 98 = 57
Example 1: Yogurt Taste Test
Add I, II, & III98 + 82 + 57 = 237IV isn(U) – n(R ⋃ O) =250 – 237 = 13
2.5-6
Copyright 2013, 2010, 2007, Pearson, Education, Inc.
Applications Involving 3 SetsThe procedure to work problems with three sets is generally the same. Start by completing region V. Next complete regions II, IV, and VI. Then complete regions I, III, and VII. Finally, complete region VIII. When you are constructing Venn diagrams, be sure to check your work carefully.
2.5-7
Copyright 2013, 2010, 2007, Pearson, Education, Inc.
Example 3: Travel PackagesLiberty Travel surveyed 125 potential customers. The following information was obtained.68 wished to travel to Hawaii.53 wished to travel to Las Vegas.47 wished to travel to Disney World.34 wished to travel to Hawaii and Las Vegas.26 wished to travel to Las Vegas and Disney World.23 wished to travel to Hawaii and Disney World.18 wished to travel to all three destinations.
2.5-8
Copyright 2013, 2010, 2007, Pearson, Education, Inc.
Example 3: Travel PackagesUse a Venn diagram to answer the following questions. How many of those surveyed a) did not wish to travel to any of these destinations?b) wished to travel only to Hawaii?c) wished to travel to Disney World and Las Vegas, but not to Hawaii?d) wished to travel to Disney World or Las Vegas, but not to Hawaii?e) wished to travel to exactly one of these destinations?
2.5-9
Copyright 2013, 2010, 2007, Pearson, Education, Inc.
Example 3: Travel PackagesSolutionV is all 3 destinations = 18II is Hawaii & Disney = 23 – 18 = 5IV is Hawaii & Vegas = 34 – 18 = 16
2.5-10
VI is Dis. & Vegas = 26 – 18 = 8I is Hawaii only = 68 – 5 – 18 – 16 = 29
Copyright 2013, 2010, 2007, Pearson, Education, Inc.
Example 3: Travel PackagesSolutionIII is Disney only = 47 – 5 – 18 – 8 = 16VII is Vegas only = 53 – 16 – 18 – 8
2.5-11
= 11
Add I – VII = 103
VIII = 125 – 103 = 22
Copyright 2013, 2010, 2007, Pearson, Education, Inc.
Example 3: Travel PackagesSolutiona) 22 did not wish to travel to any of these destinationsb) 29 wished to travel to Hawaii only
2.5-12
c) 8 wished to travel to Disney and Vegas but not Hawaii
Copyright 2013, 2010, 2007, Pearson, Education, Inc.
Example 3: Travel PackagesSolutiond) 16 + 8 + 11 = 35 wished to travel to Disney or Vegas but not Hawaiie) 29 + 16 + 11 = 56 wished to
2.5-13
to travel to exactly one of these destinations