Chapter 6: Q4. (page 215)

What is the first sentence of an indirect proof of the statement shown?
$a \geq b$

Short Answer

Expert verified

The first sentence of an indirect proof of the statement “ $a \geq b$ ” is“Assume that $a < b$ ”.

Step by step solution

Step 1. Define concept of indirect proof of the statement

An indirect proof is a proof wherein you begin by assuming temporarily that the desired conclusion is not true which then by reasoning logically reaches to a certain contradiction or some other known fact.

Step 2. Steps of writing an indirect proof

1. Assume temporarily that the conclusion is not true.

2. Reason logically until you reach a contradiction.

3. Point out that the assumption was wrong and the conclusion must then be true.

Step 3. State the first sentence of indirect proof of the statement

Consider the following statement: $a \geq b$

In order to write out the first sentence of an indirect proof of this statement, state the temporary assumption that the given conclusion is not true.

Therefore, in this case, the first sentence to be used to write this proof is: “Assume that $a < b$ ”.

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What is the first sentence of an indirect proof of the statement shown?
$a \geq b$

Short Answer

Step by step solution

Step 1. Define concept of indirect proof of the statement

Step 2. Steps of writing an indirect proof

Step 3. State the first sentence of indirect proof of the statement

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What is the first sentence of an indirect proof of the statement shown?a≥b

Short Answer

Step by step solution

Step 1. Define concept of indirect proof of the statement

Step 2. Steps of writing an indirect proof

Step 3. State the first sentence of indirect proof of the statement

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Pure Maths

Discrete Mathematics

Applied Mathematics

Theoretical and Mathematical Physics

Probability and Statistics

Logic and Functions

Study anywhere. Anytime. Across all devices.

What is the first sentence of an indirect proof of the statement shown?
$a \geq b$