2.1 Set Concepts 51 In Exercises 83–86, use the following list, which shows the 10 largest United States retailers based on 2021 sales. Let the 10 retailers in the list represent the universal set. Retailer 2021 Sales (in billions of US dollars) Walmart 460 Amazon 218 Costco 140 Home Depot 140 Kroger 136 Walgreens 108 Target 105 CVS 93 Lowe’s 88 Albertsons 72 Source: NRF.com Use the list to determine each set in roster form. 83. { } | x x is a retailer with 2021 sales less than $100 billion. { } CVS, Lowe’s, Albertsons 84. x x is a retailer with 2021 sales greater than $200 billion { } | Walmart, Amazon { } 85. { | x x is a retailer with 2021 sales between $100 billion and $200 billion} Costco, Home Depot, Kroger, Walgreens, Target { } 86. | x x { is a retailer with 2021 sales greater than $500 billion} { } or Ø In Exercises 87–90, use the following graph, created using StatCrunch, which shows the cost, in millions of dollars, of a 30-second commercial during the Super Bowl for the years 2015–2023. Let the 9 years represent the universal set. Source: Superbowl-ads.com Use the graph to determine the following sets in roster form. 87. The set of years in which the cost of a Super Bowl commercial was more than $6 million. { } 2022, 2023 88. The set of years in which the cost of a Super Bowl commercial was less than $5 million. { } 2015, 2016 89. The set of years in which the cost of a Super Bowl commercial was more than $8 million. { } or Ø 90. The set of years in which the cost of a Super Bowl commercial was between $5 million and $6 million. { } 2017, 2018, 2019, 2020, 2021 A cardinal number answers the question “How many?” An ordinal number describes the relative position that an element occupies. For example, Molly’s desk is the third desk from the aisle. In Exercises 91–94, determine whether the number used is a cardinal number or an ordinal number. 91. J. K. Rowling has written 7 Harry Potter books. Cardinal 92. Study the chart on page 25 in the book. Ordinal 93. Abraham Lincoln was the sixteenth president of the United States. Ordinal 94. Emily paid $35 for her new blouse. Cardinal Challenge Problem/Group Activity 95. a) In a given exercise, a universal set is not specified, but we know that actor Jamie Foxx is a member of the universal set. Describe five different possible universal sets of which Jamie Foxx is a member. * b) Write a description of one set that includes all the universal sets in part (a). The set of all the people in the world Research Activity 96. Georg Cantor is recognized as the founder and a leader in the development of set theory. Do research and write a paper on his life and his contributions to set theory and to the field of mathematics. *See Instructor Answer Appendix m Abraham Lincoln Library of Congress Prints and Photographs Division [LC-DIG-ppmsca-19241]. Cost (in $millions) Cost of a 30-Second Commercial During the Super Bowl 6 5 4 3 2 1 0 7 Year 4.3 5.4 5.2 5.2 5.6 5.5 6.5 7 2015 2016 2017 2018 2019 2020 2021 2022 2023 4.8
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