Geometry Laws of Detachment and Syllogism Chapter 2-4

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Questions and Answers

What does the Law of Detachment state?

  • If the hypothesis of a true conditional statement is true, then the conclusion is also true. (correct)
  • The process of using logic to draw conclusions from given facts.
  • If a car is a corvette, then it is a Chevrolet.
  • If p-->q and q-->r are true, then p-->r is also true.

What does the Law of Syllogism assert?

  • The process of using logic to draw conclusions.
  • If p-->q and q-->r are true statements, then p-->r is a true statement. (correct)
  • If a figure is a kite, then it is a quadrilateral.
  • If the hypothesis of a true conditional is true, then the conclusion is true.

What is an example of the Law of Detachment?

If a car is a corvette, then it is a Chevrolet. Suzie's car is a Corvette. Conclusion: Suzie's car is a Chevrolet.

What is deductive reasoning?

<p>The process of using logic to draw conclusions from given facts, definitions, and properties.</p> Signup and view all the answers

Provide an example of the Law of Syllogism.

<p>If a figure is a kite, then it is a quadrilateral. If a figure is a quadrilateral, then it is a polygon. Conclusion: If a figure is a kite, then it is a polygon.</p> Signup and view all the answers

How do you use the Law of Syllogism and Law of Detachment together?

<p>If you live in Fairbanks, then you live in Alaska. If you live in Alaska, then you live in the largest state in the U.S. Alan lives in Fairbanks. Conclusion: Alan lives in the largest state in the U.S.</p> Signup and view all the answers

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Study Notes

Geometry Laws Overview

  • Law of Detachment: If a true conditional statement's hypothesis is true, the conclusion also holds true.
  • Law of Syllogism: If two true conditional statements (p→q and q→r) exist, then a new true statement (p→r) can be derived.

Examples

  • Law of Detachment Example:

    • Given: "If a car is a corvette, then it is a Chevrolet."
    • Fact: "Suzie's car is a Corvette."
    • Conclusion: "Suzie's car is a Chevrolet."
  • Law of Syllogism Example:

    • Given: "If a figure is a kite, then it is a quadrilateral."
    • Given: "If a figure is a quadrilateral, then it is a polygon."
    • Conclusion: "If a figure is a kite, then it is a polygon."

Deductive Reasoning

  • Deductive reasoning involves using logic to derive conclusions from established facts, definitions, and properties.

Combined Use of Laws

  • Combined Application:
    • Given: "If you live in Fairbanks, then you live in Alaska."
    • Given: "If you live in Alaska, then you live in the largest state in the U.S."
    • Law of Syllogism Conclusion: "If you live in Fairbanks, then you live in the largest state in the U.S."
    • Law of Detachment Conclusion: "Alan lives in the largest state in the U.S." (from the previous conclusion).

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