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## Chapter 12: Draw Venn Diagrams

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**Chapter 12:**Draw Venn Diagrams**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?**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.**Fill in the region outside the loops.**Loops contain 36. H contains 46 – 36.**See what number answers the question.**How many students did not like any of these types? H contains 10 students.**Check the calculations.**7 + 4 + 6 + 3 + 9 + 5 + 2 + 10 = ?**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.