Question

To prove a theorem indirectly, we begin by assuming that its conclusion is false. List the assumption with which an indirect proof of each of the following statements would begin. Example: If a tailor wants to make a coat last, he makes the pants first. Answer: Suppose that the tailor does not make the pants first. If a chicken could talk, it would speak foul language.

Name: Problem 1, Chapter 1: Geometry
Uploaded: 2020-08-13T15:43:58-08:00
Duration: 42 s
Channel: Ian Shi
Description: To prove a theorem indirectly, we begin by assuming that its conclusion is false. List the assumption with which an indirect proof of each of the following statements would begin. Example: If a tailor wants to make a coat last, he makes the pants first. Answer: Suppose that the tailor does not make the pants first. If a chicken could talk, it would speak foul language.

   To prove a theorem indirectly, we begin by assuming that its conclusion is false. List the assumption with which an indirect proof of each of the following statements would begin.
Example: If a tailor wants to make a coat last, he makes the pants first.
Answer: Suppose that the tailor does not make the pants first.
If a chicken could talk, it would speak foul language.

Geometry

Harold R. Jacobs 2nd Edition

Chapter 1, Problem 1

Instant Answer

Solved by Expert Ian Shi

08/13/2020

Step 1

In this case, the statement is "If a chicken could talk, it would speak foul language." The opposite of this statement would be "If a chicken could talk, it would not speak foul language." Show more…

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To prove a theorem indirectly, we begin by assuming that its conclusion is false. List the assumption with which an indirect proof of each of the following statements would begin. Example: If a tailor wants to make a coat last, he makes the pants first. Answer: Suppose that the tailor does not make the pants first. If a chicken could talk, it would speak foul language.

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Key Concepts

Negation of the Conclusion

When initiating an indirect proof, the first step is to assume that the conclusion of the theorem is false. This deliberate negation forms the basis for exploring the logical consequences that ultimately reveal a contradiction, which invalidates the false assumption and confirms the original claim.

Indirect Proof

Indirect proof, also known as proof by contradiction, is a method in logic and mathematics where one assumes the negation of the statement one wishes to prove. The procedure then involves showing that this assumption leads to an inconsistency or contradiction, thereby establishing that the original statement must be true.

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