### 3.1 Sets & Set Diagrams

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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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```  ______    ______    _____    _    _    __   __
/_   _//  /_   _//  |__  //  | || | ||  \ \\/ //
`-| |,-    -| ||-     / //   | || | ||   \   //
| ||     _| ||_    / //__  | \\_/ ||   / . \\
|_||    /_____//  /_____||  \____//   /_//\_\\
`-`'    `-----`   `-----`    `---`    `-`  --`

```

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

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

```
• 26. U.S. Banking Companies

How many of the companies are not banking companies?

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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.

These comments are not screened before publication. Constructive debate about the information on this page is welcome, but personal attacks are not. Please do not post comments that are commercial in nature or that violate copyright. Comments that we regard as obscene, defamatory, or intended to incite violence will be removed. If you find a comment offensive, you may flag it.

```  _____     _____     _____      ___     _    _
|__  //   |  ___||  / ____||   / _ \\  | \  / ||
/ //    | ||__   / //---`'  | / \ || |  \/  ||
/ //__   | ||__   \ \\___    | \_/ || | .  . ||
/_____||  |_____||  \_____||   \___//  |_|\/|_||
`-----`   `-----`    `----`    `---`   `-`  `-`

```
• 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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```  _____      ___     _    _    _    _     _____