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# Section 1.6 - PowerPoint PPT Presentation

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

Survey Problems

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

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

• Determine which numbered regions make up the indicated set.

• A

U

II

IV

• Determine which numbered regions make up the indicated set.

• A – B

U

II

IV

• Determine which numbered regions make up the indicated set.

• B’ ∩ C ∩ A’

U

II

V

IV

VI

VIII

• 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

• 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

• The Venn diagram show the cardinality of each region.

• How many elements belong to set B?

U

1

7

2

3

8

• How many elements belong to set A?

U

1

7

2

3

8

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

U

1

7

2

3

8

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

U

1

7

2

3

8

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

U

1

7

2

3

8

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

U

1

7

2

3

8

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

U

1

7

2

3

8

• Classwork:

• TB pg. 55/1 – 18

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

• 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

• 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

• 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

• TB pg. 55/23

U

• TB pg. 55/25

• TB pg. 56/31

U

• 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?

Classical

Rock

7

U

7

3

5

6

Jazz

• 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

• Classwork:

• TB pg. 55/24 – 34 EVEN

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