copyright © 2014, 2010, 2007 pearson education, inc. section 2.4, slide 1 set theory 2 using...
TRANSCRIPT
Copyright © 2014, 2010, 2007 Pearson Education, Inc.Copyright © 2014, 2010, 2007 Pearson Education, Inc.
Section 2.4, Slide 1
Set Theory2
Using Mathematics to Classify Objects
Copyright © 2014, 2010, 2007 Pearson Education, Inc.Copyright © 2014, 2010, 2007 Pearson Education, Inc.
Section 2.4, Slide 2
Survey Problems2.4• Label sets in Venn diagrams with
various names
• Use Venn diagrams to solve survey problems
• Understand how to handle contradictory information in survey problems
Copyright © 2014, 2010, 2007 Pearson Education, Inc. Section 2.4, Slide 3
Naming Venn Diagrams
• We use set notation to name regions of a Venn diagram.
4 1 r B A r A B
Copyright © 2014, 2010, 2007 Pearson Education, Inc. Section 2.4, Slide 4
Naming Venn Diagrams
• Example: Name r2.
2r A B C
Copyright © 2014, 2010, 2007 Pearson Education, Inc. Section 2.4, Slide 5
Survey Problems
• When we collect and organize data into sets, we usually want to analyze the information.
• These types of problems are called survey problems.
Copyright © 2014, 2010, 2007 Pearson Education, Inc. Section 2.4, Slide 6
Survey Problems• Example: A television network conducted a market
survey. The following information on viewing habits was obtained.
(continued on next slide)
Determine how many people do not want to see reality shows and how many prefer to watch TV on the weekend?
Copyright © 2014, 2010, 2007 Pearson Education, Inc. Section 2.4, Slide 7
Survey Problems• Solution:
The universal set contains three subsets.
(continued on next slide)
Copyright © 2014, 2010, 2007 Pearson Education, Inc. Section 2.4, Slide 8
Survey Problems• Solution:
Condition (a): there are 3 people in
(continued on next slide)
.W E R
Copyright © 2014, 2010, 2007 Pearson Education, Inc. Section 2.4, Slide 9
Survey Problems• Solution:
Condition (b): there are 14 people in
(continued on next slide)
.W E
Copyright © 2014, 2010, 2007 Pearson Education, Inc. Section 2.4, Slide 10
Survey Problems• Solution:
Condition (d): 8 people want to see weekday reality shows, so 5 people have not been counted in
Condition (c): 18 have not been counted in
(continued on next slide)
.W R.R E
Copyright © 2014, 2010, 2007 Pearson Education, Inc. Section 2.4, Slide 11
Survey Problems• Solution:
Condition (e): there are 12 more members in W, 4 more in E, and 14 more in R.
Condition (h): there are 13 people outside {W, R, E}.
(continued on next slide)
Copyright © 2014, 2010, 2007 Pearson Education, Inc. Section 2.4, Slide 12
Survey Problems• Solution:
Do not want to see reality shows = 12 + 11 + 4 + 13 = 40
Prefer to watch TV on weekend =14 + 18 + 4 + 13 = 49
Copyright © 2014, 2010, 2007 Pearson Education, Inc. Section 2.4, Slide 13
Contradictions in Survey Problems• A survey problem may contain contradictory information.• Example: What web browsers are used by a sample of
people?
(continued on next slide)
Copyright © 2014, 2010, 2007 Pearson Education, Inc. Section 2.4, Slide 14
Contradictions in Survey Problems• Solution:
212 + 374 = 586 use only one of the two browsers. Contradicts (d).
Copyright © 2014, 2010, 2007 Pearson Education, Inc. Section 2.4, Slide 15
Data in Tabular Form• Example: A company sells Pilates videos. How do
customers wish to purchase the videos?
Via Access Code = web download of video
(a) Find the number of elements in
(b) Find the number of elements in
.M D.A
(continued on next slide)
Copyright © 2014, 2010, 2007 Pearson Education, Inc. Section 2.4, Slide 16
Data in Tabular Form• Example: A company sells Pilates videos. How do
customers wish to purchase the videos?
Via Access Code = web download of video
(a)
(b)