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3.1 Sets & Set Diagrams

3.1 Sets & Set Diagrams
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  • 23. Bobbleheads

    A company is conducting a survey to determine which bobblehead will generate the most sales. Participants must choose at least one bobblehead from the following list.

    • A. Albert Pujols
    • B. Drew Brees
    • C. Lebron James
    • D. Phil Mickelson

    How many different sets of choices can result from the survey?

    • Worked-Out Solution

      The general answer is as follows.

      • 1 set (A) determines 2 regions.
      • 2 sets (A, B) determine 4 regions.
      • 3 sets (A, B, C) determine 8 regions.
      • 4 sets (A, B, C, D) determine 16 regions.

      Because each person in the survey must choose at least one bobblehead, there should be 16 - 1 = 15 possible sets of choices by the respondents.

      Choose 1

      1. A
      2. B
      3. C
      4. D

      Choose 2

      1. A, B
      2. A, C
      3. A, D
      4. B, C
      5. B, D
      6. C, D

      Choose 3

      1. A, B, C
      2. A, B, D
      3. A, C, D
      4. B, C, D

      Choose 4

      1. A, B, C, D
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      _____      ___     _    _     _____     _____   
     /  ___||   / _ \\  | \  / ||  |  ___||  |__  //  
    | // __    / //\ \\ |  \/  ||  | ||__      / //   
    | \\_\ || |  ___  ||| .  . ||  | ||__     / //__  
     \____//  |_||  |_|||_|\/|_||  |_____||  /_____|| 
      `---`   `-`   `-` `-`  `-`   `-----`   `-----`  
                                                      
    
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  • 24. Bobbleheads

    A company is conducting a survey to determine which bobblehead will generate the most sales. Participants must choose at least one bobblehead from the following list.

    • A. Albert Pujols
    • B. Drew Brees
    • C. Lebron James
    • D. Phil Mickelson

    Which set diagram should the company use to display the results? Explain.

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      ______     ___     __   __    ______    _  __  
     /_   _//   / _ \\   \ \\/ //  /_   _//  | |/ // 
     `-| |,-   | / \ ||   \   //    -| ||-   | ' //  
       | ||    | \_/ ||   / . \\    _| ||_   | . \\  
       |_||     \___//   /_//\_\\  /_____//  |_|\_\\ 
       `-`'     `---`    `-`  --`  `-----`   `-` --` 
                                                     
    
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  • 25. U.S. Banking Companies

    How many of the companies are not U.S. banking companies?

    • Worked-Out Solution

      There are only 3 U.S. banking companies in the top 100. This implies that of the top 100 companies,

      are not U.S. banking companies. Do you know which three U.S. banks are in the top 100? The answer is Wells Fargo, Chase, and Bank of America.

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     _    _    _    _     _____      ___      _____   
    | |  | || | || | ||  / ____||   / _ \\   / ____|| 
    | |/\| || | || | || / //---`'  | / \ || / //---`' 
    |  /\  || | \\_/ || \ \\___    | \_/ || \ \\___   
    |_// \_||  \____//   \_____||   \___//   \_____|| 
    `-`   `-`   `---`     `----`    `---`     `----`  
                                                      
    
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  • 26. U.S. Banking Companies

    How many of the companies are not banking companies?

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       _____   _    _              _    _    _____    
      / ___// | || | ||     ___   | || | || |  __ \\  
      \___ \\ | || | ||    /   || | || | || | |  \ || 
      /    // | \\_/ ||   | [] || | \\_/ || | |__/ || 
     /____//   \____//     \__ ||  \____//  |_____//  
    `-----`     `---`       -|_||   `---`    -----`   
                             `-`                      
    
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  • 27. Top Global 100 Companies

    How many of the companies are neither U.S. companies nor banking companies?

    • Worked-Out Solution

      In the top 100, there are

      companies that are banking companies or U.S. companies. This implies that there are

      companies in the top 100 that are neither U.S. companies nor banking companies.

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     __   _      ___      ______    _____     _____   
    | || | ||   / _ \\   /_____//  |  ___||  |__  //  
    | '--' ||  / //\ \\  `____ `   | ||__      / //   
    | .--. || |  ___  || /___//    | ||__     / //__  
    |_|| |_|| |_||  |_|| `__ `     |_____||  /_____|| 
    `-`  `-`  `-`   `-`  /_//      `-----`   `-----`  
                         `-`                          
    
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  • 28. Before and After Financial Crisis

    The graph shows the value of the KBW Bank Index (ticker: BKX) from 2008 to 2010. It is intended to reflect the evolving U.S. financial sector. How do you think the set diagram will change when altered to show the list from early 2009 (during the U.S. financial crisis)? early 2008 (before the U.S. financial crisis)? Explain.

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      ______     ___      _  __     ___      ______  
     /_   _//   / _ \\   | |/ //   / _ \\   /_   _// 
     `-| |,-   / //\ \\  | ' //   | / \ ||  `-| |,-  
       | ||   |  ___  || | . \\   | \_/ ||    | ||   
       |_||   |_||  |_|| |_|\_\\   \___//     |_||   
       `-`'   `-`   `-`  `-` --`   `---`      `-`'   
                                                     
    
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