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Math
Discrete Mathematics With Applications5th Edition

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Chapter 7.2, Problem 14ES
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Discrete Mathematics With Applicat...

5th Edition
EPP + 1 other
ISBN: 9781337694193

Solutions

Chapter
Section
Problem 1TY
Problem 2TY
Problem 3TY
Problem 4TY
Problem 5TY
Problem 6TY
Problem 7TY
Problem 8TY
Problem 9TY
Problem 10TY
Problem 11TY
Problem 1ES
Problem 2ES
Problem 3ES
Problem 4ES
Problem 5ES
Problem 6ES
Problem 7ES
Problem 8ES
Problem 9ES
Problem 10ES
Problem 11ES
Problem 12ES
Problem 13ES
Problem 14ES
Problem 15ES
Problem 16ES
Problem 17ES
Problem 18ES
Problem 19ES
Problem 20ES
Problem 21ES
Problem 22ES
Problem 23ES
Problem 24ES
Problem 25ES
Problem 26ES
Problem 27ES
Problem 28ES
Problem 29ES
Problem 30ES
Problem 31ES
Problem 32ES
Problem 33ES
Problem 34ES
Problem 35ES
Problem 36ES
Problem 37ES
Problem 38ES
Problem 39ES
Problem 40ES
Problem 41ES
Problem 42ES
Problem 43ES
Problem 44ES
Problem 45ES
Problem 46ES
Problem 47ES
Problem 48ES
Problem 49ES
Problem 50ES
Problem 51ES
Problem 52ES
Problem 53ES
Problem 54ES
Problem 55ES
Problem 56ES
Problem 57ES
Problem 58ES
BuyFindarrow_forward

Discrete Mathematics With Applicat...

5th Edition
EPP + 1 other
ISBN: 9781337694193
Textbook Problem
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Explain the mistake in the following “proof.”
Theorem: The function f : Z → Z defined by the formula f ( n ) = 4 n + 3 , for each integer n, is one-to-one.
“Proof: Suppose any integer n is given. Then by definition of f, there is only one possible value for f ( n ) − namely, 4 n + 3. Hence f is one-to-one.”

To determine

To find out the mistake in the given proof.

Explanation

Given information:

Theorem: The function f:Z→Z defined by the formula f(n)=4n+3 for all integers n, is one-to-one.

Proof: Suppose any integer n is given. Then by definition of f, there is only one possible value for f(n), namely 4n+3. Hence f is one-to-one.

Calculation:

The mistake in the proof is that how it can be said that “there is only one possible value for f(n), namely 4n+3 ” without even proving it. Rather proof should have gone in the following way -

Let us suppose x,y∈Z and assume that f(x)=f(y) and now prove x=y

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Chapter 7.2,
Problem 13ES
Chapter 7.2,
Problem 15ES
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Chapter 7 Solutions

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Sect-7.1 P-1TYSect-7.1 P-2TYSect-7.1 P-3TYSect-7.1 P-4TYSect-7.1 P-5TYSect-7.1 P-6TYSect-7.1 P-7TYSect-7.1 P-8TYSect-7.1 P-9TYSect-7.1 P-1ES
Sect-7.1 P-2ESSect-7.1 P-3ESSect-7.1 P-4ESSect-7.1 P-5ESSect-7.1 P-6ESSect-7.1 P-7ESSect-7.1 P-8ESSect-7.1 P-9ESSect-7.1 P-10ESSect-7.1 P-11ESSect-7.1 P-12ESSect-7.1 P-13ESSect-7.1 P-14ESSect-7.1 P-15ESSect-7.1 P-16ESSect-7.1 P-17ESSect-7.1 P-18ESSect-7.1 P-19ESSect-7.1 P-20ESSect-7.1 P-21ESSect-7.1 P-22ESSect-7.1 P-23ESSect-7.1 P-24ESSect-7.1 P-25ESSect-7.1 P-26ESSect-7.1 P-27ESSect-7.1 P-28ESSect-7.1 P-29ESSect-7.1 P-30ESSect-7.1 P-31ESSect-7.1 P-32ESSect-7.1 P-33ESSect-7.1 P-34ESSect-7.1 P-35ESSect-7.1 P-36ESSect-7.1 P-37ESSect-7.1 P-38ESSect-7.1 P-39ESSect-7.1 P-40ESSect-7.1 P-41ESSect-7.1 P-42ESSect-7.1 P-43ESSect-7.1 P-44ESSect-7.1 P-45ESSect-7.1 P-46ESSect-7.1 P-47ESSect-7.1 P-48ESSect-7.1 P-49ESSect-7.1 P-50ESSect-7.1 P-51ESSect-7.1 P-52ESSect-7.1 P-53ESSect-7.2 P-1TYSect-7.2 P-2TYSect-7.2 P-3TYSect-7.2 P-4TYSect-7.2 P-5TYSect-7.2 P-6TYSect-7.2 P-7TYSect-7.2 P-8TYSect-7.2 P-9TYSect-7.2 P-10TYSect-7.2 P-11TYSect-7.2 P-1ESSect-7.2 P-2ESSect-7.2 P-3ESSect-7.2 P-4ESSect-7.2 P-5ESSect-7.2 P-6ESSect-7.2 P-7ESSect-7.2 P-8ESSect-7.2 P-9ESSect-7.2 P-10ESSect-7.2 P-11ESSect-7.2 P-12ESSect-7.2 P-13ESSect-7.2 P-14ESSect-7.2 P-15ESSect-7.2 P-16ESSect-7.2 P-17ESSect-7.2 P-18ESSect-7.2 P-19ESSect-7.2 P-20ESSect-7.2 P-21ESSect-7.2 P-22ESSect-7.2 P-23ESSect-7.2 P-24ESSect-7.2 P-25ESSect-7.2 P-26ESSect-7.2 P-27ESSect-7.2 P-28ESSect-7.2 P-29ESSect-7.2 P-30ESSect-7.2 P-31ESSect-7.2 P-32ESSect-7.2 P-33ESSect-7.2 P-34ESSect-7.2 P-35ESSect-7.2 P-36ESSect-7.2 P-37ESSect-7.2 P-38ESSect-7.2 P-39ESSect-7.2 P-40ESSect-7.2 P-41ESSect-7.2 P-42ESSect-7.2 P-43ESSect-7.2 P-44ESSect-7.2 P-45ESSect-7.2 P-46ESSect-7.2 P-47ESSect-7.2 P-48ESSect-7.2 P-49ESSect-7.2 P-50ESSect-7.2 P-51ESSect-7.2 P-52ESSect-7.2 P-53ESSect-7.2 P-54ESSect-7.2 P-55ESSect-7.2 P-56ESSect-7.2 P-57ESSect-7.2 P-58ESSect-7.3 P-1TYSect-7.3 P-2TYSect-7.3 P-3TYSect-7.3 P-4TYSect-7.3 P-5TYSect-7.3 P-1ESSect-7.3 P-2ESSect-7.3 P-3ESSect-7.3 P-4ESSect-7.3 P-5ESSect-7.3 P-6ESSect-7.3 P-7ESSect-7.3 P-8ESSect-7.3 P-9ESSect-7.3 P-10ESSect-7.3 P-11ESSect-7.3 P-12ESSect-7.3 P-13ESSect-7.3 P-14ESSect-7.3 P-15ESSect-7.3 P-16ESSect-7.3 P-17ESSect-7.3 P-18ESSect-7.3 P-19ESSect-7.3 P-20ESSect-7.3 P-21ESSect-7.3 P-22ESSect-7.3 P-23ESSect-7.3 P-24ESSect-7.3 P-25ESSect-7.3 P-26ESSect-7.3 P-27ESSect-7.3 P-28ESSect-7.3 P-29ESSect-7.3 P-30ESSect-7.4 P-1TYSect-7.4 P-2TYSect-7.4 P-3TYSect-7.4 P-4TYSect-7.4 P-5TYSect-7.4 P-6TYSect-7.4 P-7TYSect-7.4 P-8TYSect-7.4 P-9TYSect-7.4 P-1ESSect-7.4 P-2ESSect-7.4 P-3ESSect-7.4 P-4ESSect-7.4 P-5ESSect-7.4 P-6ESSect-7.4 P-7ESSect-7.4 P-8ESSect-7.4 P-9ESSect-7.4 P-10ESSect-7.4 P-11ESSect-7.4 P-12ESSect-7.4 P-13ESSect-7.4 P-14ESSect-7.4 P-15ESSect-7.4 P-16ESSect-7.4 P-17ESSect-7.4 P-18ESSect-7.4 P-19ESSect-7.4 P-20ESSect-7.4 P-21ESSect-7.4 P-22ESSect-7.4 P-23ESSect-7.4 P-24ESSect-7.4 P-25ESSect-7.4 P-26ESSect-7.4 P-27ESSect-7.4 P-28ESSect-7.4 P-29ESSect-7.4 P-30ESSect-7.4 P-31ESSect-7.4 P-32ESSect-7.4 P-33ESSect-7.4 P-34ESSect-7.4 P-35ESSect-7.4 P-36ESSect-7.4 P-37ESSect-7.4 P-38ES
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