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Discrete Mathematics An Introduction to Mathematical Reasoning Brief Edition

# TEXTBOOK SOLUTIONS FOR Discrete Mathematics An Introduction to Mathematical Reasoning Brief Edition 1st Edition

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SAMPLE SOLUTION
Chapter: Problem:
• Step 1 of 8

Let us consider the definition of congruence modulo 3

If a and b are the integers, then a is congruent to b modulo 3;
• Step 2 of 8
Provided 3 divides the number
• Step 3 of 8
Now, the numbers are as follows
• Step 4 of 8
• Step 5 of 8
(a) Let us consider the following expression
• Step 6 of 8
Since, 3 divides the number, by definition we can say that
• Step 7 of 8

(b) Now, consider the following equation.

……(1)

From the calculations in part (a), we can say that

Or

……(2)

Thus, from equations (1) and (2),

• Step 8 of 8

(c) Let us consider the division of 25 by 3

The equation shows that the remainder when 25 is divided by 3 is 1

Also consider the division of 19 by 3

The equation shows that the remainder when 19 is divided by 3 is 1

Thus, 25 and 19 have the same remainder when divided by 3.

Corresponding Textbook

Discrete Mathematics An Introduction to Mathematical Reasoning Brief Edition | 1st Edition
9780495826170ISBN-13: 0495826170ISBN: Susanna S. EppAuthors:
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