section 2.5 application of sets

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Section 2.5

Application of Sets


What You Will Learn

Application of Sets

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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

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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?


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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.


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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


Add I, II, & III98 + 82 + 57 = 237IV isn(U) – n(R ⋃ O) =250 – 237 = 13

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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.

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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.

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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?

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Example 3: Travel PackagesSolutionV is all 3 destinations = 18II is Hawaii & Disney = 23 – 18 = 5IV is Hawaii & Vegas = 34 – 18 = 16

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VI is Dis. & Vegas = 26 – 18 = 8I is Hawaii only = 68 – 5 – 18 – 16 = 29


Example 3: Travel PackagesSolutionIII is Disney only = 47 – 5 – 18 – 8 = 16VII is Vegas only = 53 – 16 – 18 – 8

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= 11

Add I – VII = 103

VIII = 125 – 103 = 22


Example 3: Travel PackagesSolutiona) 22 did not wish to travel to any of these destinationsb) 29 wished to travel to Hawaii only

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c) 8 wished to travel to Disney and Vegas but not Hawaii


Example 3: Travel PackagesSolutiond) 16 + 8 + 11 = 35 wished to travel to Disney or Vegas but not Hawaiie) 29 + 16 + 11 = 56 wished to

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to travel to exactly one of these destinations

section 2.5 application of sets

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