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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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