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Discrete Mathematics With Applicat...

5th Edition
EPP + 1 other
ISBN: 9781337694193

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BuyFindarrow_forward

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

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.

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 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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Sect-9.1 P-7ESSect-9.1 P-8ESSect-9.1 P-9ESSect-9.1 P-10ESSect-9.1 P-11ESSect-9.1 P-12ESSect-9.1 P-13ESSect-9.1 P-14ESSect-9.1 P-15ESSect-9.1 P-16ESSect-9.1 P-17ESSect-9.1 P-18ESSect-9.1 P-19ESSect-9.1 P-20ESSect-9.1 P-21ESSect-9.1 P-22ESSect-9.1 P-23ESSect-9.1 P-24ESSect-9.1 P-25ESSect-9.1 P-26ESSect-9.1 P-27ESSect-9.1 P-28ESSect-9.1 P-29ESSect-9.1 P-30ESSect-9.1 P-31ESSect-9.1 P-32ESSect-9.1 P-33ESSect-9.2 P-1TYSect-9.2 P-2TYSect-9.2 P-3TYSect-9.2 P-4TYSect-9.2 P-5TYSect-9.2 P-6TYSect-9.2 P-1ESSect-9.2 P-2ESSect-9.2 P-3ESSect-9.2 P-4ESSect-9.2 P-5ESSect-9.2 P-6ESSect-9.2 P-7ESSect-9.2 P-8ESSect-9.2 P-9ESSect-9.2 P-10ESSect-9.2 P-11ESSect-9.2 P-12ESSect-9.2 P-13ESSect-9.2 P-14ESSect-9.2 P-15ESSect-9.2 P-16ESSect-9.2 P-17ESSect-9.2 P-18ESSect-9.2 P-19ESSect-9.2 P-20ESSect-9.2 P-21ESSect-9.2 P-22ESSect-9.2 P-23ESSect-9.2 P-24ESSect-9.2 P-25ESSect-9.2 P-26ESSect-9.2 P-27ESSect-9.2 P-28ESSect-9.2 P-29ESSect-9.2 P-30ESSect-9.2 P-31ESSect-9.2 P-32ESSect-9.2 P-33ESSect-9.2 P-34ESSect-9.2 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