Chapter 12:

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• Chapter 12
• Draw Venn Diagrams

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• In a poll of 46 students, 23 liked rap music, 24
  liked rock music, and 19 liked country music. Of
  all the students, 12 liked rap and country, 13
  liked rap and rock, and 14 liked country and
  rock. Of those students, 9 liked all three types
  of music. How many students did not like any of
  these types?

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Draw loops for the categories.
4
Fill loops from the inside out.
9 in all three loops.
D contains 12 9.
B contains 13 9.
F contains 14 9.
G contains 19 (9 3 5).
C contains 24 18.
A contains 23 16.
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Fill in the region outside the loops.
Loops contain 36.
H contains 46 36.
6
See what number answers the question.
How many students did not like any of these types?
H contains 10 students.
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Check the calculations.
7 4 6 3 9 5 2 10 ?
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Strategy Draw Venn diagrams

• Draw overlapping loops for intersecting sets.

• Fill regions from the inside out.
• Subtract carefully.
• After regions are filled, see what number answers
  the question.
  
• Check the calculations.