   Chapter 9.4, Problem 6ES ### Discrete Mathematics With Applicat...

5th Edition
EPP + 1 other
ISBN: 9781337694193

#### Solutions

Chapter
Section ### Discrete Mathematics With Applicat...

5th Edition
EPP + 1 other
ISBN: 9781337694193
Textbook Problem
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# (a) Given any set of seven integers, must there be two that have the same remainder when divided by 6? Why? (b)Given any set of seven integers, must there be two that have the same remainder when divided by 8? Why?

To determine

(a)

To check:

Whether there must be two integers that have the same remainder when divided by 6, if there is any set of seven integers.

Explanation

Given information:

There is any set of seven integers.

Concept used:

The pigeonhole principle states that if n+1 objects (e.g. pigeons) are to be distributed in n holes then some hole must contain at least two objects (pigeons).

Calculation:

Consider any set of seven integers

To determine

(b)

To check:

Whether there must be two integers that have the same remainder when divided by 8, if there is any set of seven integers.

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