2.4 Venn Diagrams with Three Sets and Verification of Equality of Sets 77 13. A {1, 3, 4, 5, 9, 10} 14. U 15. C {4, 5, 6, 8, 9, 11} 16. B′ {1, 2, 9, 10, 11, 13} 17. >A B {3, 4, 5} 18. >A C {4, 5, 9} 19. >B C ( )′ {1, 2, 3, 7, 9, 10, 11, 12, 13, 14} 20. > > A B C {4, 5} 21. <A C ( )′ {2, 7, 12, 13, 14} 22. > < A B C ( ) {3, 4, 5, 9} 23. A B ( ) − ′ {2, 3, 4, 5, 6, 7, 8, 11, 12, 13, 14} 24. A B ′ − {2, 11, 13} 25. Olympic Medals Consider the following table, which shows countries that won at least 15 medals in the 2022 Winter Olympics. Let the countries in the table represent the universal set. Note that ROC stands for Russian Olympic Committee. Country Gold Medals Silver Medals Bronze Medals Total Medals Norway 16 8 13 37 ROC 6 12 14 32 Germany 12 10 5 27 Canada 4 8 14 26 United States 8 10 7 25 Sweden 8 5 5 18 Austria 7 7 4 18 Japan 3 6 9 18 Netherlands 8 5 4 17 Italy 2 7 8 17 China 9 4 2 15 Switzerland 7 2 6 15 Let A the set of countries = that won at least 10 gold medals. Let B the set of countries = that won at least 8 silver medals. Let C the set of countries = that won at least 6 bronze medals. Construct a Venn diagram that illustrates the set A B, , and C. * 26. Olympic Medals Use the data in the table from Exercise 25. Let the countries in the table represent the universal set. Let A the set of countries = that won at least 20 total medals. Let B the set of countries = that won between 5 and 10 gold medals, inclusive. Let C the set of countries = that won between 5 and 10 silver medals, inclusive. Construct a Venn diagram that illustrates the set A B, , and C. * {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14} Source: Olympics.com Grain Production In Exercises 27–32, use the following table, which shows the top 10 countries for production of corn, rice, and wheat in 2022. The universal set is the set of countries in the world. Rankings of Corn, Rice, and Wheat Production in 2022 Corn Rice Wheat 1. United States 1. China 1. China 2. China 2. India 2. India 3. Brazil 3. Bangladesh 3. Russia 4. Argentina 4. Indonesia 4. United States 5. Indonesia 5. Vietnam 5. Canada 6. Ukraine 6. Thailand 6. France 7. India 7. Myanmar 7. Pakistan 8. Mexico 8. Philippines 8. Ukraine 9. Romania 9. Brazil 9. Germany 10. Russia 10. Cambodia 10. Turkey Indicate in which regions, I–VIII in Fig. 2.22, each of the following countries belongs. 27. United States IV 28. Indonesia II 29. India V 30. France VII 31. Nigeria VIII 32. Argentina I Source: FAO.org Corn Rice Wheat I II III IV V VI VII VIII U Figure 2.22 *See Instructor Answer Appendix I II III IV V VI VII VIII U Figures that measure less than in. across Blue figures Circles 1 4 Figure 2.23 Figures In Exercises 33– 44, indicate in Fig. 2.23 the region in which each of the figures should be placed.
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