   Chapter 9.4, Problem 9ES ### 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
1 views

# (a) If seven integers are chosen from between 1 and 12 inclusive, must at least one of them be odd? Why? (b)If ten integers are chosen from between 1 and 20 inclusive, must at least one of them be even? Why?

To determine

(a)

To check:

Whether there must be at least one of them be odd, if seven integers are chosen from between 1 and 12 inclusive.

Explanation

Given information:

The given set is {1,2,3,4,5,6,7,8,9,10,11,12}.

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 the problem that if seven integers are chosen from between 1 and 12 inclusive then objective is show that at least one them must be odd

To determine

(b)

To check:

Whether there must be at least one of them be even, if ten integers are chosen from between 1 and 20 inclusive.

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