   Chapter 9.3, Problem 24ES ### 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
8 views

# (a) How many integers from 1 through 1,000 are multiples of 2 or multiples of 9? (b) Suppose an integer from 1 through 1,000 is chosen at random. Use the result o part (a) to find the probability that the integer is a multiple of 2 or a multiple of 9. (c) How many integers from 1 through 1,000 are neither multiples of 2 nor multiples of 9?

To determine

(a)

To find the number of integers from 1 through 1,000 are multiples of 2 or multiples of 9.

Explanation

Given information:

Let A= the set of all integers from 1 through 1000 that are multiple of 2.

Let B= the set of all integers from 1 through 1000 that are multiple of 9.

Then

AB= the set of all integers from 1 through 1000 that are multiple of 2 or multiple of 9 and

AB= the set of all integers from 1 through 1000 that are multiple of both 2 and 9.

= the set of all integers from 1 through 1000 that are multiple of 18.

Concept used:

N(AB)=N(A)+N(B)N(AB)

Calculation:

Let A= the set of all integers from 1 through 1000 that are multiple of 4.

Let B= the set of all integers from 1 through 1000 that are multiple of 7.

Then

AB= the set of all integers from 1 through 1000 that are multiple of 7 or multiple of 4 and

AB= the set of all integers from 1 through 1000 that are multiple of both 7 and 4.

= the set of all integers from 1 through 1000 that are multiple of 28.

Every integer from 1 through 1000 is a multiple of 2, each can be represented in the form 2k, for some integer k from 1 through 500

To determine

(b)

To find the probability that the integer is a multiple of 2 or a multiple of 9 using part (a).

To determine

(c)

To find the number of integers from 1 through 1000 are neither multiples of 2 nor multiples of 9.

### Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

#### The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started 