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Elements Of Modern Algebra

8th Edition
Gilbert + 2 others
ISBN: 9781285463230

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Section
BuyFindarrow_forward

Elements Of Modern Algebra

8th Edition
Gilbert + 2 others
ISBN: 9781285463230
Textbook Problem

Prove that if a is positive and a b is negative, then b is negative.

To determine

To prove: If a is positive and ab is negative, then b is negative.

Explanation

Formula used:

i) contains a subset +, called the positive integers, which has the following properties:

a) + is closed under addition.

b) + is closed under multiplication.

c) For each x, one and only one of the following statements is true: x+ x+ x=0.

Proof:

Let a be positive and ab be negative.

On the contrary, suppose that b is not negative.

Thus, either b=0 or b+

Case i) If b=0

Then ab=a0=0

This is a contradiction to ab is negative

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