   Chapter A.3, Problem 29E Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085

Solutions

Chapter
Section Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085
Textbook Problem

In Exercises 29 to 32, the claims made are not always true. Cite a counterexample to show why each claims fails.If a < b , then a ⋅ c < b ⋅ c .

To determine

To prove:

The given claims made are not always true and give counter example.

Explanation

Consider the following claim,

“If a<b, then ac<bc.”

Multiplication:

1) If a<b and c>0 that is c is positive then ac<bc.

2) If a<b and c<0 that is c is negative then ac>bc.

By using the multiplication property if a<b then ac<bc only when c>0 that is c is positive.

Example:

Let assume that a=2,b=3

Since by given condition c>0.

But assume that the value of c=1

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