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Get Full Access to Discrete Mathematics With Applications - 4 Edition - Chapter 4.3 - Problem 14e
Get Full Access to Discrete Mathematics With Applications - 4 Edition - Chapter 4.3 - Problem 14e

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# Fill in the blanks in the following proof that for all

ISBN: 9780495391326 48

## Solution for problem 14E Chapter 4.3

Discrete Mathematics with Applications | 4th Edition

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Problem 14E

Problem 14E

Fill in the blanks in the following proof that for all integers a and b, if a | b then a | (−b).

Proof:

Suppose a and b are any integers such that (a). By definition of divisibility, there exists an integer r such that (b) By substitution.

b = −ar = a(r).

Let t = (c) Then t is an integer because t = (1)• r, and both 1 and r are integers. Thus, by substitution, −b = at, where t is an integer, and so by definition of divisibility, (d), as was to be shown.

Step-by-Step Solution:

SOLUTION
Step 1

Given result is, for all integers

Step 2 of 2

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