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3.3 Deductive & Inductive Reasoning

3.3 Deductive & Inductive Reasoning
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  • 1. Brown v. Board of Education

    Complete the syllogism. Then draw a set diagram to represent the syllogism. (see Example 1.)

    Brown v. Board of Education

    • Premise: All unequal public schools are unconstitutional.
    • Premise: All segregated public schools are unequal.
    • Conclusion: _______________________________________
    • Worked-Out Solution

      The syllogism is completed as follows.

      Brown v. Board of Education

      • Premise: All unequal public schools are unconstitutional.
      • Premise: All segregated public schools are unequal.
      • Conclusion: All segregated public schools are unconstitutional.

      There is more than one way to represent the premises and conclusions with a set diagram. Here is one way.

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     ______      ___      _____      ___     _    _   
|      \\   / _ \\   |__  //    / _ \\  | |  | || 
|  --  //  | / \ ||    / //    | / \ || | |/\| || 
|  --  \\  | \_/ ||   / //__   | \_/ || |  /\  || 
|______//   \___//   /_____||   \___//  |_// \_|| 
`------`    `---`    `-----`    `---`   `-`   `-`
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  • 2. Citizens United v. Federal Election Commission

    Complete the syllogism. Then draw a set diagram to represent the syllogism. (See Example 1.)

    Citizens United v. Federal Election Commission

    • Premise: Any law that limits free speech is unconstitutional.
    • Premise: Any corporate spending on independent political broadcasts is free speech.
    • Conclusion: _______________________________________
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     _    _     ______    _____     ______   _    _   
| |  | ||  /_   _//  |__  //   /_   _// | |  | || 
| |/\| ||   -| ||-     / //     -| ||-  | |/\| || 
|  /\  ||   _| ||_    / //__    _| ||_  |  /\  || 
|_// \_||  /_____//  /_____||  /_____// |_// \_|| 
`-`   `-`  `-----`   `-----`   `-----`  `-`   `-`
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  • 3. Marbury v. Madison

    Use the excerpt from the Supreme Court's majority opinion in the case Marbury v. Madison.

    "If, then, the courts are to regard the Constitution, and the Constitution is superior to any ordinary act of the legislature, the Constitution, and not such ordinary act, must govern the case to which they both apply."

    Marbury v. Madison, 5 U.S. 137, 177, 178 (1803)

    Suppose the Constitution is superior to any ordinary law. Also, suppose that an ordinary law conflicts with the Constitution. What conclusion can you draw? (See Example 1 and Example 2.)

    • Worked-Out Solution

      Here is one possible syllogism that can be written to arrive at a conclusion.

      Marbury v. Madison

      • Premise: If an ordinary law conflicts with the Constitution, then because the Constitution is superior to ordinary law, the Constitution will govern the case to which they both apply.
      • Premise: An ordinary law conflicts with the Constitution.
      • Conclusion: The Constitution will govern the case to which they both apply.
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      ______    _____     _____      ___      _____   
 /_   _//  |  ___||  |__  //    / _ \\   / ____|| 
 `-| |,-   | ||__      / //    | / \ || / //---`' 
   | ||    | ||__     / //__   | \_/ || \ \\___   
   |_||    |_____||  /_____||   \___//   \_____|| 
   `-`'    `-----`   `-----`    `---`     `----`
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  • 4. Marbury v. Madison

    Use the excerpt from the Supreme Court's majority opinion in the case Marbury v. Madison.

    "If, then, the courts are to regard the Constitution, and the Constitution is superior to any ordinary act of the legislature, the Constitution, and not such ordinary act, must govern the case to which they both apply."

    Marbury v. Madison, 5 U.S. 137, 177,178 (1803)

    Explain why the Constitution must be considered superior to any ordinary law for the Supreme Court to conclude that any unconstitutional law is illegal. (See Example 1 and Example 2.)

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    __    __   __   __     _____   __   __            
\ \\ / //  \ \\/ //   / ___//  \ \\/ //   ____    
 \ \/ //    \ ` //    \___ \\   \ ` //   |    \\  
  \  //      | ||     /    //    | ||    | [] ||  
   \//       |_||    /____//     |_||    |  __//  
    `        `-`'   `-----`      `-`'    |_|`-`   
                                         `-`
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  • 5. United States v. Virginia

    Write a syllogism that involves the Supreme Court's decision.(See Example 1 and Example 2.)

    In United States v. Virginia, the Supreme Court held that the Virginia Military Institute's male-only admission policy was unconstitutional because it treated women unequally.

    • Worked-Out Solution

      Here is one possible syllogism that can be written to arrive at a conclusion.

      United States v. Virginia

      • Premise: All unequal treatment of individuals based on gender is unconstitutional.
      • Premise: The Virginia Military Institute's male-only admission policy was an unequal treatment of individuals that was based on gender.
      • Conclusion: The Virginia Military Institute's male-only admission policy was unconstitutional.
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      ______   __   __             _    _    __   _   
 /_   _//  \ \\/ //   ____    | || | || | || | || 
 `-| |,-    \ ` //   |    \\  | || | || | '--' || 
   | ||      | ||    | [] ||  | \\_/ || | .--. || 
   |_||      |_||    |  __//   \____//  |_|| |_|| 
   `-`'      `-`'    |_|`-`     `---`   `-`  `-`  
                     `-`
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  • 6. Miranda v. Arizona

    Write a syllogism that involves the Supreme Court's decision. (See Example 1 and Example 2.)

    In Miranda v. Arizona, the Supreme Court held that statements made by Ernesto Miranda were inadmissible because Miranda had not been advised of his Fifth Amendment rights before he made the statements.

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      _____      ___      ____       ___      ______  
 /  ___||   / _ \\   |  _ \\    / _ \\   /_____// 
| // __    / //\ \\  | |_| ||  | / \ ||  `____ `  
| \\_\ || |  ___  || | .  //   | \_/ ||  /___//   
 \____//  |_||  |_|| |_|\_\\    \___//   `__ `    
  `---`   `-`   `-`  `-` --`    `---`    /_//     
                                         `-`
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  • 7. Georgia v. Randolph

    Write a syllogism that involves the Supreme Court's decision.(See Example 1 and Example 2.)

    In Georgia v. Randolph, the Supreme Court held that it was unconstitutional for police to search a house without a warrant if one resident consents but another resident objects.

    • Worked-Out Solution

      Here is one possible syllogism that can be written to arrive at a conclusion.

      Georgia v. Randolph

      • Premise: If any resident of a house objects to a police search without a warrant, then it is unconstitutional for the police to search the house.
      • Premise: In the case of Georgia v. Randolph, one resident objected to a police search of the house without a warrant.
      • Conclusion: The police search of the house without a warrant was unconstitutional (regardless of the fact that another resident of the same house agreed to the search).
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      ______    _____     _____     _____     ____    
 /_   _//  |  ___||  /  ___||  |  ___||  |  _ \\  
   | ||    | ||__   | // __    | ||__    | |_| || 
  _| ||    | ||__   | \\_\ ||  | ||__    | .  //  
 /__//     |_____||  \____//   |_____||  |_|\_\\  
 `--`      `-----`    `---`    `-----`   `-` --`
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  • 8. Roper v. Simmons

    Write a syllogism that involves the Supreme Court's decision. (See Example 1 and Example 2.)

    In Roper v. Simmons, the Supreme Court held that the execution of an offender who was under 18 years old at the time of the crime was "cruel and unusual punishment" and therefore unconstitutional.

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     _    _      ___    __    __    ______   _    _   
| |  | ||   / _ \\  \ \\ / //  /_   _// | || | || 
| |/\| ||  / //\ \\  \ \/ //    -| ||-  | || | || 
|  /\  || |  ___  ||  \  //     _| ||_  | \\_/ || 
|_// \_|| |_||  |_||   \//     /_____//  \____//  
`-`   `-` `-`   `-`     `      `-----`    `---`
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