Discrete Mathematics With Applicat...

5th Edition

EPP + 1 other

ISBN: 9781337694193

Textbook Problem

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(a) How many integers from 1 through 1,000 are multiples of 4 or multiples of 7?
(b) Suppose an integer from 1 through 1,000 is chosen at random. Use the result of part (a) to find the probability that the integer is a multiple of 4 or a multiple of 7.
(c) How many integers from 1 through 1,000 are neither multiples of 4 nor multiples of 7?

To determine

(a)

To find the number of integers from 1 through 1000 are multiples of 4 or multiples of 7.

Explanation

Given information:

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

A∪B= The set of all integers from 1 through 1000 that are multiple of 7 or multiple of 4 and

A∩B= 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.

Concept used:

N(A∪B)=N(A)+N(B)−N(A∩B)

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

A∪B= The set of all integers from 1 through 1000 that are multiple of 7 or multiple of 4 and

A∩B= 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 4, each can be represented in the form 4k, for some integer k from 1 through 250

To determine

(b)

To find the probability that the integer is a multiple of 4 or a multiple of 7 using part (a).

To determine

(c)

To find the number of integers from 1 through 1000 are neither multiples of 4 nor multiples of 7.

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Chapter 9 Solutions

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Sect-9.1 P-1TY Sect-9.1 P-2TY Sect-9.1 P-3TY Sect-9.1 P-4TY Sect-9.1 P-1ES Sect-9.1 P-2ES Sect-9.1 P-3ES Sect-9.1 P-4ES Sect-9.1 P-5ES Sect-9.1 P-6ES

Sect-9.1 P-7ES Sect-9.1 P-8ES Sect-9.1 P-9ES Sect-9.1 P-10ES Sect-9.1 P-11ES Sect-9.1 P-12ES Sect-9.1 P-13ES Sect-9.1 P-14ES Sect-9.1 P-15ES Sect-9.1 P-16ES Sect-9.1 P-17ES Sect-9.1 P-18ES Sect-9.1 P-19ES Sect-9.1 P-20ES Sect-9.1 P-21ES Sect-9.1 P-22ES Sect-9.1 P-23ES Sect-9.1 P-24ES Sect-9.1 P-25ES Sect-9.1 P-26ES Sect-9.1 P-27ES Sect-9.1 P-28ES Sect-9.1 P-29ES Sect-9.1 P-30ES Sect-9.1 P-31ES Sect-9.1 P-32ES Sect-9.1 P-33ES Sect-9.2 P-1TY Sect-9.2 P-2TY Sect-9.2 P-3TY Sect-9.2 P-4TY Sect-9.2 P-5TY Sect-9.2 P-6TY Sect-9.2 P-1ES Sect-9.2 P-2ES Sect-9.2 P-3ES Sect-9.2 P-4ES Sect-9.2 P-5ES Sect-9.2 P-6ES Sect-9.2 P-7ES Sect-9.2 P-8ES Sect-9.2 P-9ES Sect-9.2 P-10ES Sect-9.2 P-11ES Sect-9.2 P-12ES Sect-9.2 P-13ES Sect-9.2 P-14ES Sect-9.2 P-15ES Sect-9.2 P-16ES Sect-9.2 P-17ES Sect-9.2 P-18ES Sect-9.2 P-19ES Sect-9.2 P-20ES Sect-9.2 P-21ES Sect-9.2 P-22ES Sect-9.2 P-23ES Sect-9.2 P-24ES Sect-9.2 P-25ES Sect-9.2 P-26ES Sect-9.2 P-27ES Sect-9.2 P-28ES Sect-9.2 P-29ES Sect-9.2 P-30ES Sect-9.2 P-31ES Sect-9.2 P-32ES Sect-9.2 P-33ES Sect-9.2 P-34ES Sect-9.2 P-35ES Sect-9.2 P-36ES Sect-9.2 P-37ES Sect-9.2 P-38ES Sect-9.2 P-39ES Sect-9.2 P-40ES Sect-9.2 P-41ES Sect-9.2 P-42ES Sect-9.2 P-43ES Sect-9.2 P-44ES Sect-9.2 P-45ES Sect-9.2 P-46ES Sect-9.2 P-47ES Sect-9.3 P-1TY Sect-9.3 P-2TY Sect-9.3 P-3TY Sect-9.3 P-4TY Sect-9.3 P-5TY Sect-9.3 P-1ES Sect-9.3 P-2ES Sect-9.3 P-3ES Sect-9.3 P-4ES Sect-9.3 P-5ES Sect-9.3 P-6ES Sect-9.3 P-7ES Sect-9.3 P-8ES Sect-9.3 P-9ES Sect-9.3 P-10ES Sect-9.3 P-11ES Sect-9.3 P-12ES Sect-9.3 P-13ES Sect-9.3 P-14ES Sect-9.3 P-15ES Sect-9.3 P-16ES Sect-9.3 P-17ES Sect-9.3 P-18ES Sect-9.3 P-19ES Sect-9.3 P-20ES Sect-9.3 P-21ES Sect-9.3 P-22ES Sect-9.3 P-23ES Sect-9.3 P-24ES Sect-9.3 P-25ES Sect-9.3 P-26ES Sect-9.3 P-27ES Sect-9.3 P-28ES Sect-9.3 P-29ES Sect-9.3 P-30ES Sect-9.3 P-31ES Sect-9.3 P-32ES Sect-9.3 P-33ES Sect-9.3 P-34ES Sect-9.3 P-35ES Sect-9.3 P-36ES Sect-9.3 P-37ES Sect-9.3 P-38ES Sect-9.3 P-39ES Sect-9.3 P-40ES Sect-9.3 P-41ES Sect-9.3 P-42ES Sect-9.3 P-43ES Sect-9.3 P-44ES Sect-9.3 P-45ES Sect-9.3 P-46ES Sect-9.3 P-47ES Sect-9.3 P-48ES Sect-9.3 P-49ES Sect-9.4 P-1TY Sect-9.4 P-2TY Sect-9.4 P-3TY Sect-9.4 P-3ES Sect-9.4 P-4ES Sect-9.4 P-5ES Sect-9.4 P-6ES Sect-9.4 P-7ES Sect-9.4 P-8ES Sect-9.4 P-9ES Sect-9.4 P-10ES Sect-9.4 P-11ES Sect-9.4 P-12ES Sect-9.4 P-13ES Sect-9.4 P-14ES Sect-9.4 P-15ES Sect-9.4 P-16ES Sect-9.4 P-17ES Sect-9.4 P-18ES Sect-9.4 P-19ES Sect-9.4 P-20ES Sect-9.4 P-21ES Sect-9.4 P-22ES Sect-9.4 P-23ES Sect-9.4 P-24ES Sect-9.4 P-25ES Sect-9.4 P-26ES Sect-9.4 P-27ES Sect-9.4 P-28ES Sect-9.4 P-29ES Sect-9.4 P-30ES Sect-9.4 P-31ES Sect-9.4 P-32ES Sect-9.4 P-33ES Sect-9.4 P-34ES Sect-9.4 P-35ES Sect-9.4 P-36ES Sect-9.4 P-37ES Sect-9.4 P-38ES Sect-9.4 P-39ES Sect-9.4 P-40ES Sect-9.5 P-1TY Sect-9.5 P-2TY Sect-9.5 P-3TY Sect-9.5 P-4TY Sect-9.5 P-5TY Sect-9.5 P-1ES Sect-9.5 P-2ES Sect-9.5 P-3ES Sect-9.5 P-4ES Sect-9.5 P-5ES Sect-9.5 P-6ES Sect-9.5 P-7ES Sect-9.5 P-8ES Sect-9.5 P-9ES Sect-9.5 P-10ES Sect-9.5 P-11ES Sect-9.5 P-12ES Sect-9.5 P-13ES Sect-9.5 P-14ES Sect-9.5 P-15ES Sect-9.5 P-16ES Sect-9.5 P-17ES Sect-9.5 P-18ES Sect-9.5 P-19ES Sect-9.5 P-20ES Sect-9.5 P-21ES Sect-9.5 P-22ES Sect-9.5 P-23ES Sect-9.5 P-24ES Sect-9.5 P-25ES Sect-9.5 P-26ES Sect-9.5 P-27ES Sect-9.5 P-28ES Sect-9.5 P-29ES Sect-9.5 P-30ES Sect-9.6 P-1TY Sect-9.6 P-2TY Sect-9.6 P-3TY Sect-9.6 P-1ES Sect-9.6 P-2ES Sect-9.6 P-3ES Sect-9.6 P-4ES Sect-9.6 P-5ES Sect-9.6 P-6ES Sect-9.6 P-7ES Sect-9.6 P-8ES Sect-9.6 P-9ES Sect-9.6 P-10ES Sect-9.6 P-11ES Sect-9.6 P-12ES Sect-9.6 P-13ES Sect-9.6 P-14ES Sect-9.6 P-15ES Sect-9.6 P-16ES Sect-9.6 P-17ES Sect-9.6 P-18ES Sect-9.6 P-19ES Sect-9.6 P-20ES Sect-9.6 P-21ES Sect-9.7 P-1TY Sect-9.7 P-2TY Sect-9.7 P-3TY Sect-9.7 P-4TY Sect-9.7 P-5TY Sect-9.7 P-6TY Sect-9.7 P-7TY Sect-9.7 P-1ES Sect-9.7 P-2ES Sect-9.7 P-3ES Sect-9.7 P-4ES Sect-9.7 P-5ES Sect-9.7 P-6ES Sect-9.7 P-7ES Sect-9.7 P-8ES Sect-9.7 P-9ES Sect-9.7 P-10ES Sect-9.7 P-11ES Sect-9.7 P-12ES Sect-9.7 P-13ES Sect-9.7 P-14ES Sect-9.7 P-15ES Sect-9.7 P-16ES Sect-9.7 P-17ES Sect-9.7 P-18ES Sect-9.7 P-19ES Sect-9.7 P-20ES Sect-9.7 P-21ES Sect-9.7 P-22ES Sect-9.7 P-23ES Sect-9.7 P-24ES Sect-9.7 P-25ES Sect-9.7 P-26ES Sect-9.7 P-27ES Sect-9.7 P-28ES Sect-9.7 P-29ES Sect-9.7 P-30ES Sect-9.7 P-31ES Sect-9.7 P-32ES Sect-9.7 P-33ES Sect-9.7 P-34ES Sect-9.7 P-35ES Sect-9.7 P-36ES Sect-9.7 P-37ES Sect-9.7 P-38ES Sect-9.7 P-39ES Sect-9.7 P-40ES Sect-9.7 P-41ES Sect-9.7 P-42ES Sect-9.7 P-43ES Sect-9.7 P-44ES Sect-9.7 P-45ES Sect-9.7 P-46ES Sect-9.7 P-47ES Sect-9.7 P-48ES Sect-9.7 P-49ES Sect-9.7 P-50ES Sect-9.7 P-51ES Sect-9.7 P-52ES Sect-9.7 P-53ES Sect-9.7 P-54ES Sect-9.7 P-55ES Sect-9.8 P-1TY Sect-9.8 P-2TY Sect-9.8 P-3TY Sect-9.8 P-4TY Sect-9.8 P-5TY Sect-9.8 P-1ES Sect-9.8 P-2ES Sect-9.8 P-3ES Sect-9.8 P-4ES Sect-9.8 P-5ES Sect-9.8 P-6ES Sect-9.8 P-7ES Sect-9.8 P-8ES Sect-9.8 P-9ES Sect-9.8 P-10ES Sect-9.8 P-11ES Sect-9.8 P-12ES Sect-9.8 P-13ES Sect-9.8 P-14ES Sect-9.8 P-15ES Sect-9.8 P-16ES Sect-9.8 P-17ES Sect-9.8 P-18ES Sect-9.8 P-19ES Sect-9.8 P-20ES Sect-9.8 P-21ES Sect-9.8 P-22ES Sect-9.8 P-23ES Sect-9.9 P-1TY Sect-9.9 P-2TY Sect-9.9 P-3TY Sect-9.9 P-4TY Sect-9.9 P-1ES Sect-9.9 P-2ES Sect-9.9 P-3ES Sect-9.9 P-4ES Sect-9.9 P-5ES Sect-9.9 P-6ES Sect-9.9 P-7ES Sect-9.9 P-8ES Sect-9.9 P-9ES Sect-9.9 P-10ES Sect-9.9 P-11ES Sect-9.9 P-12ES Sect-9.9 P-13ES Sect-9.9 P-14ES Sect-9.9 P-15ES Sect-9.9 P-16ES Sect-9.9 P-17ES Sect-9.9 P-18ES Sect-9.9 P-19ES Sect-9.9 P-20ES Sect-9.9 P-21ES Sect-9.9 P-22ES Sect-9.9 P-23ES Sect-9.9 P-24ES Sect-9.9 P-25ES Sect-9.9 P-26ES Sect-9.9 P-27ES Sect-9.9 P-28ES Sect-9.9 P-29ES Sect-9.9 P-30ES Sect-9.9 P-31ES Sect-9.9 P-32ES Sect-9.9 P-33ES Sect-9.9 P-34ES

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