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3.2 Statements & Negations

3.2 Statements & Negations
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  • 23. ENERGY STAR Label

    Use a set diagram to analyze the statement about ENERGY STAR.

    The ENERGY STAR label was established to

    • reduce greenhouse gas emissions and other pollutants caused by the inefficient use of energy and
    • make it easy for consumers to identify and purchase energy-efficient products that offer savings on energy bills without sacrificing performance, features, and comfort.
    • Worked-Out Solution

      Here is one way to draw a set diagram that represents the statement.

      Notice that it is possible that a product that does not have the ENERGY STAR label can still pass both requirements and lie in the intersection of the blue and pink regions.

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      ____      _____    _    _      ___      _____   
     |  _ \\   |  ___|| | || | ||   / _ \\   / ____|| 
     | |_| ||  | ||__   | || | ||  / //\ \\ / //---`' 
     | .  //   | ||__   | \\_/ || |  ___  ||\ \\___   
     |_|\_\\   |_____||  \____//  |_||  |_|| \_____|| 
     `-` --`   `-----`    `---`   `-`   `-`   `----`  
                                                      
    
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  • 24. ENERGY STAR Rebates

    Use a set diagram to analyze the statement about ENERGY STAR.

    ENERGY STAR Rebates

    Each state and territory will choose dollar amounts for the products selected. Most rebate amounts range from $50 to $500, depending upon the product being purchased, the purchase price, and other potential market factors. Some states give additional rebates for recycling.

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      ______    ______   __   __   _    _    _____    
     /_   _//  /_   _//  \ \\/ // | || | || |  __ \\  
       | ||     -| ||-    \   //  | || | || | |  \ || 
      _| ||     _| ||_    / . \\  | \\_/ || | |__/ || 
     /__//     /_____//  /_//\_\\  \____//  |_____//  
     `--`      `-----`   `-`  --`   `---`    -----`   
                                                      
    
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  • 25. CO2e Emissions

    Use the graph to write one statement involving "all" and "some" that you can make about the products in the graph. Use a set diagram to analyze the statement.

    • Worked-Out Solution

      Here is a possible statement that you could make.

      All the products shown emit less than 50 grams of CO2e, while some emit less than 10 grams.

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     __   __   __   __               ___      _____   
     \ \\/ //  \ \\/ //     ___     / _ \\   /  ___|| 
      \   //    \ ` //     /   ||  | / \ || | // __   
      / . \\     | ||     | [] ||  | \_/ || | \\_\ || 
     /_//\_\\    |_||      \__ ||   \___//   \____//  
     `-`  --`    `-`'       -|_||   `---`     `---`   
                             `-`                      
    
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  • 26. Planned Purchases

    Use a set diagram to visualize the negation of the statement about planned purchases.

    To help heat my apartment, I will buy a space heater and an electric fireplace, or I will buy an ENERGY STAR qualified woodstove.

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     _    _     ______   __   __     ___     _____    
    | \  / ||  /_   _//  \ \\/ //   / _ \\  |  __ \\  
    |  \/  ||   -| ||-    \   //   | / \ || | |  \ || 
    | .  . ||   _| ||_    / . \\   | \_/ || | |__/ || 
    |_|\/|_||  /_____//  /_//\_\\   \___//  |_____//  
    `-`  `-`   `-----`   `-`  --`   `---`    -----`   
                                                      
    
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  • 27. Planned Purchases

    Use a set diagram to visualize the negation of the statement about planned purchases.

    To update my plumbing, I will buy a solar water heater or a gas condensing water heater, and low-flow showerheads.

    • Worked-Out Solution

      Here is one way to visualize the original statement and its negation.

       

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      ______    _____     _____    __   __    ______  
     /_   _//  |  ___||  /  ___||  \ \\/ //  /_   _// 
       | ||    | ||__   | // __     \ ` //     | ||   
      _| ||    | ||__   | \\_\ ||    | ||     _| ||   
     /__//     |_____||  \____//     |_||    /__//    
     `--`      `-----`    `---`      `-`'    `--`     
                                                      
    
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  • 28. Planned Purchases

    Use a set diagram to visualize the negation of the statement about planned purchases.

    For my new home, I will buy a chest freezer or an upright freezer, and fluorescent lighting or ENERGY STAR LED lighting.

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     _    _    __   __   _    _    _    _             
    | |  | ||  \ \\/ // | || | || | || | ||   ____    
    | |/\| ||   \ ` //  | || | || | || | ||  |    \\  
    |  /\  ||    | ||   | \\_/ || | \\_/ ||  | [] ||  
    |_// \_||    |_||    \____//   \____//   |  __//  
    `-`   `-`    `-`'     `---`     `---`    |_|`-`   
                                             `-`      
    
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