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Section 1.6. Survey Problems. Objectives. Use Venn diagrams to visualize a survey’s results. Use survey results to complete Venn diagrams and answer questions about the survey. Example 1:. Determine which numbered regions make up the indicated set. A. U. II. IV. Example 2:.

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Section 1 6

Section 1.6

Survey Problems


Objectives
Objectives

  • Use Venn diagrams to visualize a survey’s results.

  • Use survey results to complete Venn diagrams and answer questions about the survey.


Example 1
Example 1:

  • Determine which numbered regions make up the indicated set.

    • A

U

II

IV


Example 2
Example 2:

  • Determine which numbered regions make up the indicated set.

    • A – B

U

II

IV


Example 3
Example 3:

  • Determine which numbered regions make up the indicated set.

    • B’ ∩ C ∩ A’

U

II

V

IV

VI

VIII


Example 4
Example 4:

  • If n(A) = 21, n(B) = 29, and n(U) = 48, find the number of elements in each regions I, III, and IV.

U

II 7

IV


Example 5
Example 5:

  • If n(A) = 23, n(B) = 27, and n(U) = 53, find the number of elements in each regions I, III, and IV.

U

II 8

IV


Example 6
Example 6:

  • The Venn diagram show the cardinality of each region.

    • How many elements belong to set B?

U

1

7

2

3

8


Example 7
Example 7:

  • How many elements belong to set A?

U

1

7

2

3

8


Example 8
Example 8:

  • How many elements belong to set A but not set C?

U

1

7

2

3

8


Example 9
Example 9:

  • How many elements belong to set B but not set A?

U

1

7

2

3

8


Example 10
Example 10:

  • How many elements belong to set A or set C?

U

1

7

2

3

8


Example 11
Example 11:

  • How many elements belong to set A and set C, but not to set B?

U

1

7

2

3

8


Example 12
Example 12:

  • Considering sets A, B, and C, how many elements belong to exactly one of these sets?

U

1

7

2

3

8


Section 1 6 assignment
Section 1.6 Assignment

  • Classwork:

    • TB pg. 55/1 – 18

      • Must write problems and show ALL work to receive credit for the given assignment.


Example 13
Example 13:

  • The accompanying Venn diagram shows the number of elements in region V. Use the given cardinalities to determine the number of elements in each of the other seven regions.

    • n(U) = 30, n(A) = 11, n(B) = 8, n(C) = 14, n(A∩B) = 3, n(A∩C) = 5, n(B∩C) = 3

U

2


Example 14
Example 14:

  • n(U) = 32, n(A) = 21, n(B) = 15, n(C) = 14, n(A∩B) = 6, n(A∩C) = 7, n(B∩C) = 8

U

2


Example 15
Example 15:

  • n(U) = 38, n(A) = 26, n(B) = 21, n(C) = 18, n(A∩B) =17, n(A∩C) = 11, n(B∩C) = 8, n(A∩B∩C) = 7

U


Example 16
Example 16:

  • TB pg. 55/23

U


Example 17
Example 17:

  • TB pg. 55/25


Example 18
Example 18:

  • TB pg. 56/31

U


Example 19
Example 19:

  • A survey of 80 college students was taken to determine the musical styles they listened to. Forty-two students listened to rock, 34 listened to classical, and 27 to jazz. Twelve students listened to rock and jazz, 14 to rock and classical, and 10 to classical and jazz. Seven students listened to all three musical styles.

    • Of those surveyed,

      • How many listened to only rock music?

      • How many listened to classical and jazz, but not rock?

      • How many listened to classical or jazz, but not rock?

      • How many listened to music in exactly one of the musical styles?

      • How many listened to music in at least two of the musical styles?

      • How many did not listen to any of the musical styles?


Example 191
Example 19:

Classical

Rock

7

U

7

3

5

6

Jazz


Example 192
Example 19:

  • Of those surveyed,

    • How many listened to only rock music? 23

    • How many listened to classical and jazz, but not rock? 3

    • How many listened to classical or jazz, but not rock? 32

    • How many listened to music in exactly one of the musical styles? 52

    • How many listened to music in at least two of the musical styles?22

    • How many did not listen to any of the musical styles? 6


Section 1 6 assignment1
Section 1.6 Assignment

  • Classwork:

    • TB pg. 55/24 – 34 EVEN

      • Must write problems and show ALL work to receive credit for the given assignment.


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