Chapter 6: Q3. (page 216)

Suppose someone plans to write an indirect proof of the conditional. Write a correct first sentence of the indirect proof.
If $a \neq b$ , then $a - b \neq 0$ .

Short Answer

Expert verified

The correct first sentence would be “Assume that $a - b = 0$ .”

Step by step solution

Step 1. Apply the concept of indirect proof.

The indirect proof is based on the classical notion that any given sentence, such as the conclusion, must be either true or false. The Indirect proof is done by assuming the premises to be true and the conclusion to be false and deriving a contradiction.

Step 2. Step description.

Consider the statement.

If $a \neq b$ then $a - b \neq 0$ .

If someone wants to write an indirect proof for this statement then there is a need to write a correct first sentence of this indirect proof.

Step 3. Step description.

The correct first sentence of the indirect proof is, Assume that $a - b = 0$ .

Therefore, the correct first sentence of this indirect proof is “Assume that $a - b = 0$ .”

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Suppose someone plans to write an indirect proof of the conditional. Write a correct first sentence of the indirect proof.
If $a \neq b$ , then $a - b \neq 0$ .

Short Answer

Step by step solution

Step 1. Apply the concept of indirect proof.

Step 2. Step description.

Step 3. Step description.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Decision Maths

Mechanics Maths

Theoretical and Mathematical Physics

Calculus

Logic and Functions

Pure Maths

Study anywhere. Anytime. Across all devices.

Suppose someone plans to write an indirect proof of the conditional. Write a correct first sentence of the indirect proof.If a≠b, then a−b≠0.

Short Answer

Step by step solution

Step 1. Apply the concept of indirect proof.

Step 2. Step description.

Step 3. Step description.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Decision Maths

Mechanics Maths

Theoretical and Mathematical Physics

Calculus

Logic and Functions

Pure Maths

Study anywhere. Anytime. Across all devices.

Suppose someone plans to write an indirect proof of the conditional. Write a correct first sentence of the indirect proof.
If $a \neq b$ , then $a - b \neq 0$ .