Sets Assignment: The exercise questions are found in the booklet Exercise set, page 55. Exercise 1-14: 3, 12, 13 Exercise 15-24: 16 to 24 Exercise 25-36: 25, 26, 30, 29, 34 Exercise 37-48: 41, 43, 47, 48 Exercise 53-62: 53, 55, 58, 62 Exercise 63-70: 64, 68 Exercise 71-82: 71, 75, 78SECTION 2.1 | Basic Properties of Sets 55 EXERCISE SET 2.1 . In Exercises I to 14, use the roster method to write each 41. {January, March, May, July, August, October, December} of the given sets. For some exercises you may need to consult a reference, such as the Internet or an encyclopedia. 42. {Iowa, Ohio, Utah} 1. The set of U.S. coins with a value of less than 50c 43. {Arizona, Alabama, Arkansas, Alaska} 2. The set of months of the year with a name that ends 44. (Mexico, Canada} with the letter y 45. {spring, summer} 3. The set of planets in our solar system with a name that 46. {1900, 1901, 1902, 1903, 1904, .... 1999} starts with the letter M 47. The set of months that have less than 31 days 4. The set of the seven dwarfs 48. (1, 2, 3, 4, 5, ...) 5. The set of U.S. presidents who have served after 49 Average Student Debt The following bar Bill Clinton graph shows the average student debt in each 6. The set of months with exactly 30 days graduating class from 2008 to 2015. 7. The set of negative integers greater than -6 8. The set of whole numbers less than 8 40 9. The set of integers x that satisfy x - 4 = 3 35 10. The set of integers x that satisfy 2x - 1 = -11 30 Debt (in thousands of dollars) 11. The set of natural numbers x that satisfy x + 4 = 1 25 12. The set of whole numbers x that satisfy x - 1 0} 2012 34. 0 ED 2011 Year 35. (2, 3, 4) = (2, 2, 3, 4, 4) 2010 36. (5, 6, 7) ~ (9, 20, 31) 2009 In Exercises 37 to 48, use set-builder notation to write 2008 each of the following sets. 2007 37. {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12} 0 200 400 600 800 1000 1200 1400 1600 1800 38. (45, 55, 65, 75) Price (in dollars per troy ounce) 39. {5, 10, 15} Average yearly price of gold 40. {1, 4, 9, 16, 25, 36, 49, 64, 81} SOURCE: U.S. Geological Survey, U.S. Department of the Interior56 CHAPTER 2 | Sets Use the information in the graph and the roster method Use the information in the table and the roster method to represent each of the following sets. to represent each of the following sets. a. The set of years in which the price of gold was a. The set of years in which the winning time was greater than $1500. greater than 2 minutes 3.00 seconds. b. The set of years in which the price of gold was b. The set of years in which the winning time was greater than $1000 but less than $1500. less than 2 minutes 3.50 seconds but greater than c. The set of years in which the price of gold was less 2 minutes 3.00 seconds. than $1000. c. The year in which the winning time was the least of 51. Gasoline Prices The following broken line all the given times. graph shows the average U.S. monthly regular In Exercises 53 to 62, find the cardinality of each of the gasoline prices for the months from January to following sets. For some exercises you may need to consult November of 2015. a reference, such as the Internet or an encyclopedia. 53. A = (2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22} 2.90 54. B = (7, 14, 21, 28, 35, 42, 49, 56} 55. D = the set of all dogs that can spell "elephant" 270 56. S = the set of all states in the United States 2.50 57. J = the set of all states of the United States that border Price (in dollars per gallon) Minnesota 2.30 58. T = the set of all stripes on the U.S. flag 2.10 59. N = the set of all baseball teams in the National League 60. C = the set of all chess pieces on a chess board at the May Jun ful start of a chess game Aug sep Nov 61. {3, 6, 9, 12, 15, ..., 363} Average monthly U.S. regular gasoline prices in 2015 62. {7, 1 1, 15, 19, 23, 27, ..., 407} SOURCE: U.S. Energy Information Administration In Exercises 63 to 70, state whether each of the given Use the information in the above graph and the roster pairs of sets are equal, equivalent, both, or neither. method to represent each of the following sets. 63. The set of U.S. senators; the set of U.S. representatives a. The set of months in which the price of gasoline was 64. The set of single-digit natural numbers; the set of pins greater than $2.50 per gallon. used in a regulation bowling game b. The set of months in which the price of gasoline was 65. The set of positive whole numbers; the set of natural greater than $2.30 but less than $2.60 per gallon. numbersc. The set of months in which the price of gasoline was 66. The set of single-digit natural numbers; the set of less than $2.20 per gallon. single-digit integers 52. Winning Times The following table shows the 67. {1, 2, 3); {1, II, III} winning times in the Kentucky Derby from 2006 68. {6, 8, 10, 12}; {1, 2, 3, 4} to 2015. 69. {2, 5); 40, 1} 70. { }; 40} Winning times in minutes:seconds In Exercises 71 to 82, determine whether each of the sets Year Time Year Time is a well-defined set. 2006 2:01.36 2011 2:02.04 71. The set of good foods 2007 2:02.17 2012 2:01.83 72. The set of the six most heavily populated cities in the United States 2008 2:01.82 2013 2:02.89 73. The set of tall buildings in the city of Chicago 2009 2:02.66 2014 2:03.66 74. The set of states that border Colorado 2010 2:04.45 2015 2:03.02 75. The set of even integers SOURCE: http://horseracing.about.com/