Geometry Laws of Detachment and Syllogism Chapter 2-4

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?

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

Provide an example of the Law of Syllogism.

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. Signup and view all the answers

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

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. Signup and view all the answers

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).

Description

Explore the fundamental laws of logic in geometry with this flashcard quiz. Dive into the Law of Detachment and the Law of Syllogism to understand how logical conclusions are derived from true statements. Perfect for reinforcing your understanding of these crucial concepts in geometry.