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3.2 Statements & Negations

3.2 Statements & Negations
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  • 1. Social Networking

    Use a set diagram to analyze the statement about a social networking website.(See Example 1 and Example 2.)

    You own all the content and information that you post.

    • Worked-Out Solution

      When you are using a set diagram to help analyze and understand a statement, remember that your goal is to analyze and understand the statement! The goal is not to draw a certain style or type of set diagram. Most people who use set diagrams effectively develop their own style. For some people, the style is informal ... more like doodling than formal mathematics.

      With that said, here are a couple of ways that the statement can be represented with a set diagram.

      Notice that the set diagram helps you see the following.

      1. If you post content and information, then you own it.
      2. You can also own content and information that you have not posted.

      When you are trying to analyze a statement, don't get hung up on deciding whether the statement is true. That is a different matter. Before deciding whether it is true or false, your first goal should be to simply understand what the statement is saying.

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      ______   _    _     _  __   __   __    _____   
     /_   _// | || | ||  | |/ //  \ \\/ //  |__  //  
     `-| |,-  | || | ||  | ' //    \ ` //     / //   
       | ||   | \\_/ ||  | . \\     | ||     / //__  
       |_||    \____//   |_|\_\\    |_||    /_____|| 
       `-`'     `---`    `-` --`    `-`'    `-----`  
                                                     
    
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  • 2. Social Networking

    Use a set diagram to analyze the statement about a social networking website. (See Example 1 and Example 2.)

    All businesses can join the website and create fan clubs.

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     _____      ______  __    __   __   __    ____    
    |  __ \\   /_   _// \ \\ / //  \ \\/ //  |  _ \\  
    | |  \ ||   -| ||-   \ \/ //    \ ` //   | |_| || 
    | |__/ ||   _| ||_    \  //      | ||    | .  //  
    |_____//   /_____//    \//       |_||    |_|\_\\  
     -----`    `-----`      `        `-`'    `-` --`  
                                                      
    
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  • 3. Web Site Policy

    Use a set diagram to analyze the statement about a social networking website.(See Example 1 and Example 2)

    All individuals can join the website, post pictures, and manage their privacy settings.

    • Worked-Out Solution

      When you are using a set diagram to help analyze and understand a statement, remember that your goal is to analyze and understand the statement! The goal is not to draw a certain style or type of set diagram. Most people who use set diagrams effectively develop their own style. For some people, the style is informal ... more like doodling than formal mathematics.

      With that said, here is one way that the statement can be represented with a group of three set diagrams.

      To begin, you need to make an assumption as to what the phrase "all individuals" means. One would guess that this means "any human being." So, the statement says nothing about dogs, horses, or other animals.

      Stating something clearly so that it is understood in only one way is difficult. That is why there are attorneys who work at writing contracts and other statements. It is also why we have courts, such as the Supreme Court, whose job it is to decide exactly what is meant by legal documents.

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     _    _      ___      _  __     ___      _____   
    | |  | ||   / _ \\   | |/ //   / _ \\   /  ___|| 
    | |/\| ||  / //\ \\  | ' //   / //\ \\ | // __   
    |  /\  || |  ___  || | . \\  |  ___  ||| \\_\ || 
    |_// \_|| |_||  |_|| |_|\_\\ |_||  |_|| \____//  
    `-`   `-` `-`   `-`  `-` --` `-`   `-`   `---`   
                                                     
    
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  • 4. Text Message Notifications

    Use a set diagram to analyze the statement about a social networking website. (See Example 1 and Example 2.)

    You can receive a text message notification on your phone for every friend request and every email you receive on the website.

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      ______     ___       _____     ___     _    _   
     /_   _//   / _ \\    / ___//   / _ \\  | \  / || 
       | ||    | / \ ||   \___ \\  | / \ || |  \/  || 
      _| ||    | \_/ ||   /    //  | \_/ || | .  . || 
     /__//      \___//   /____//    \___//  |_|\/|_|| 
     `--`       `---`   `-----`     `---`   `-`  `-`  
                                                      
    
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  • 5. Illegal Website Activity

    Use a set diagram to analyze the statement about a social networking website.(See Example 1 and Example 2)

    You will not conduct any contests on the website without prior authorization from the website administrators. All unauthorized contests found will be considered illegal activity and will be terminated. Your membership may also be terminated.

    • Worked-Out Solution

      There are many ways to use set diagrams to help analyze statements like this. If a single diagram becomes too cumbersome, you might find it more helpful to analyze parts of the statement separately.

      This set diagram makes it clear that:

      (a) All unauthorized contests will be terminated.

      (b) Other things can be terminated, too.

      This set diagram makes it clear that:

      (a) Unauthorized contests on the website are considered illegal activity.

      (b) There can be other types of illegal activity.

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     ______      ___      ______    _____    _____    
    |      \\   / _ \\   /_   _//  |  ___|| |  __ \\  
    |  --  //  / //\ \\    | ||    | ||__   | |  \ || 
    |  --  \\ |  ___  ||  _| ||    | ||__   | |__/ || 
    |______// |_||  |_|| /__//     |_____|| |_____//  
    `------`  `-`   `-`  `--`      `-----`   -----`   
                                                      
    
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  • 6. Burger Fans

    Use a set diagram to analyze the statement about a social networking website. (See Example 1 and Example 2.)

    A fast food restaurant has a fan page for its avocado burger and a separate fan page for its jalapeno burger. Every member who is a "fan" of both burgers will receive a coupon for a free burger of his or her choice.

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      ______    ______             __   __    ______  
     /_____//  /_   _//   ____     \ \\/ //  /_   _// 
     `____ `    -| ||-   |    \\    \ ` //     | ||   
     /___//     _| ||_   | [] ||     | ||     _| ||   
     `__ `     /_____//  |  __//     |_||    /__//    
     /_//      `-----`   |_|`-`      `-`'    `--`     
     `-`                 `-`                          
    
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  • 7. Burger Fans

    Add the following information to your set diagram in Exercise 6. (See Example 1 and Example 2.)

    All members who are fans of the avocado burger, jalapeno burger, and veggie burger are eligible for a grand prize.

    • Worked-Out Solution

      Because the statement uses and, it means people who are members of all three fan clubs are eligible for the grand prize.


      Remember the goal is to draw relationships that help you question a statement and possibly go back and reword the statement so that any ambiguity is removed.

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      _____      ___     __   __     ___       _____  
     |__  //    / _ \\   \ \\/ //   / _ \\    / ___// 
       / //    / //\ \\   \   //   / //\ \\   \___ \\ 
      / //__  |  ___  ||  / . \\  |  ___  ||  /    // 
     /_____|| |_||  |_|| /_//\_\\ |_||  |_|| /____//  
     `-----`  `-`   `-`  `-`  --` `-`   `-` `-----`   
                                                      
    
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  • 8. Privacy Settings

    The recommended privacy settings on a social networking website are shown.

    1. Use a set diagram to analyze the different categories of members. Indicate what parts of your profile are accessible to each region in the set diagram.
    2. You have a circle of friends that you frequently spend time with as a group. Where in the set diagram are these friends most likely located?
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      _____      ___       _____    _____    _    _   
     / ____||   / _ \\    / ___//  |  ___|| | || | || 
    / //---`'  / //\ \\   \___ \\  | ||__   | || | || 
    \ \\___   |  ___  ||  /    //  | ||__   | \\_/ || 
     \_____|| |_||  |_|| /____//   |_____||  \____//  
      `----`  `-`   `-` `-----`    `-----`    `---`   
                                                      
    
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