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Chapter 6: Q3. (page 215)

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

Doug is a Canadian.

Short Answer

Expert verified

The first sentence of an indirect proof of the statement 鈥淒oug is a Canadian.鈥� is鈥淎ssume that Doug is not a Canadian.鈥�

Step by step solution

01

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.

02

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.

03

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

Consider the following statement:Doug is a Canadian.

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: 鈥淎ssume that Doug is not a Canadian.鈥�

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Most popular questions from this chapter

Complete the following statement with the word always, sometimes, or never.

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Arrange sentences (a)-(e) in an order that completes an indirect proof of the following statement: In a plane, two lines perpendicular to a third line are parallel to each other.

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