   Chapter 9.5, Problem 15ES ### 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) How many even integer are in the set { 1 , 2 , 3 , ... , 100 } ? (b) How many odd integers are in the set { 1 , 2 , 3 , ... , 100 } ? (c) How many ways can two integers be selected from the set { 1 , 2 , 3 , ... , 100 } so that their sum is even?(d) How many ways can two integers be selected from the set { 1 , 2 , 3 , ... , 100 } so that their sum is odd?

To determine

(a)

The number of even integers in the set {1,2,3,.....,100}.

Explanation

Given information:

The set of integers

{1,2,3,.....,100}

Concept used:

Those integers which are divided by 2 are called even integers.

Calculation:

One integer is either even or odd. Generally even and odd integers are occurred alternately. 1 is odd, 2 is even, 3 is odd, 4 is even and so on.

Proceeding in that way we can say half of the total number of integers given in the set is even.

Total number of integers in the set {1,2,3,

To determine

(b)

The number of odd integers in the set {1,2,3,.....,100}.

To determine

(c)

The number of ways can two integers be selected from the set {1,2,3,.....,100} so that their sum is even.

To determine

(d)

The number of ways can two integers be selected from the set {1,2,3,.....,100} so that their sum is odd.

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