Discrete Mathematics With Applicat...

5th Edition

EPP + 1 other

ISBN: 9781337694193

Textbook Problem

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a. Use mathematical induction to prove that if n is any integer with n ≥ 1 , then for every integer m ≥ 1 , n m ≥ 1 .
b. Prove that if n is any integer with n ≥ 1 , then n r ≤ n s for all integers r and s with r ≤ s .

To determine

(a)

To prove:

That nm≥1 for every integer m≥1, for any integer n≥1, using the mathematical induction.

Explanation

Given information:

The integers n and m are given as n≥1 and m≥1.

Proof:

First, let’s consider when m=1 ,

→nm=1=n1=n

Because n≥1 is a given condition, nm≥1 is true for m=1.

Then, let’s assume that the result is true for m=p where p≥1.

→nm=p=np≥1

Now, for m=p+1 ,

→nm=p+1

To determine

(b)

To prove:

That nr≤ns for all integer r and s where r≤s for any integer n≥1.

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Chapter 11 Solutions

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Sect-11.1 P-1TY Sect-11.1 P-2TY Sect-11.1 P-3TY Sect-11.1 P-4TY Sect-11.1 P-5TY Sect-11.1 P-6TY Sect-11.1 P-1ES Sect-11.1 P-2ES Sect-11.1 P-3ES Sect-11.1 P-4ES

Sect-11.1 P-5ES Sect-11.1 P-6ES Sect-11.1 P-7ES Sect-11.1 P-8ES Sect-11.1 P-9ES Sect-11.1 P-10ES Sect-11.1 P-11ES Sect-11.1 P-12ES Sect-11.1 P-13ES Sect-11.1 P-14ES Sect-11.1 P-15ES Sect-11.1 P-16ES Sect-11.1 P-17ES Sect-11.1 P-18ES Sect-11.1 P-19ES Sect-11.1 P-20ES Sect-11.1 P-21ES Sect-11.1 P-22ES Sect-11.1 P-23ES Sect-11.1 P-24ES Sect-11.1 P-25ES Sect-11.1 P-26ES Sect-11.1 P-27ES Sect-11.1 P-28ES Sect-11.2 P-1TY Sect-11.2 P-2TY Sect-11.2 P-3TY Sect-11.2 P-4TY Sect-11.2 P-5TY Sect-11.2 P-6TY Sect-11.2 P-1ES Sect-11.2 P-2ES Sect-11.2 P-3ES Sect-11.2 P-4ES Sect-11.2 P-5ES Sect-11.2 P-6ES Sect-11.2 P-7ES Sect-11.2 P-8ES Sect-11.2 P-9ES Sect-11.2 P-10ES Sect-11.2 P-11ES Sect-11.2 P-12ES Sect-11.2 P-13ES Sect-11.2 P-14ES Sect-11.2 P-15ES Sect-11.2 P-16ES Sect-11.2 P-17ES Sect-11.2 P-18ES Sect-11.2 P-19ES Sect-11.2 P-20ES Sect-11.2 P-21ES Sect-11.2 P-22ES Sect-11.2 P-23ES Sect-11.2 P-24ES Sect-11.2 P-25ES Sect-11.2 P-26ES Sect-11.2 P-27ES Sect-11.2 P-28ES Sect-11.2 P-29ES Sect-11.2 P-30ES Sect-11.2 P-31ES Sect-11.2 P-32ES Sect-11.2 P-33ES Sect-11.2 P-34ES Sect-11.2 P-35ES Sect-11.2 P-36ES Sect-11.2 P-37ES Sect-11.2 P-38ES Sect-11.2 P-39ES Sect-11.2 P-40ES Sect-11.2 P-41ES Sect-11.2 P-42ES Sect-11.2 P-43ES Sect-11.2 P-44ES Sect-11.2 P-45ES Sect-11.2 P-46ES Sect-11.2 P-47ES Sect-11.2 P-48ES Sect-11.2 P-49ES Sect-11.2 P-50ES Sect-11.2 P-51ES Sect-11.3 P-1TY Sect-11.3 P-2TY Sect-11.3 P-3TY Sect-11.3 P-1ES Sect-11.3 P-2ES Sect-11.3 P-3ES Sect-11.3 P-4ES Sect-11.3 P-5ES Sect-11.3 P-6ES Sect-11.3 P-7ES Sect-11.3 P-8ES Sect-11.3 P-9ES Sect-11.3 P-10ES Sect-11.3 P-11ES Sect-11.3 P-12ES Sect-11.3 P-13ES Sect-11.3 P-14ES Sect-11.3 P-15ES Sect-11.3 P-16ES Sect-11.3 P-17ES Sect-11.3 P-18ES Sect-11.3 P-19ES Sect-11.3 P-20ES Sect-11.3 P-21ES Sect-11.3 P-22ES Sect-11.3 P-23ES Sect-11.3 P-24ES Sect-11.3 P-25ES Sect-11.3 P-26ES Sect-11.3 P-27ES Sect-11.3 P-28ES Sect-11.3 P-29ES Sect-11.3 P-30ES Sect-11.3 P-31ES Sect-11.3 P-32ES Sect-11.3 P-33ES Sect-11.3 P-34ES Sect-11.3 P-35ES Sect-11.3 P-36ES Sect-11.3 P-37ES Sect-11.3 P-38ES Sect-11.3 P-39ES Sect-11.3 P-40ES Sect-11.3 P-41ES Sect-11.3 P-42ES Sect-11.3 P-43ES Sect-11.4 P-1TY Sect-11.4 P-2TY Sect-11.4 P-3TY Sect-11.4 P-4TY Sect-11.4 P-5TY Sect-11.4 P-1ES Sect-11.4 P-2ES Sect-11.4 P-3ES Sect-11.4 P-4ES Sect-11.4 P-5ES Sect-11.4 P-6ES Sect-11.4 P-7ES Sect-11.4 P-8ES Sect-11.4 P-9ES Sect-11.4 P-10ES Sect-11.4 P-11ES Sect-11.4 P-12ES Sect-11.4 P-13ES Sect-11.4 P-14ES Sect-11.4 P-15ES Sect-11.4 P-16ES Sect-11.4 P-17ES Sect-11.4 P-18ES Sect-11.4 P-19ES Sect-11.4 P-20ES Sect-11.4 P-21ES Sect-11.4 P-22ES Sect-11.4 P-23ES Sect-11.4 P-24ES Sect-11.4 P-25ES Sect-11.4 P-26ES Sect-11.4 P-27ES Sect-11.4 P-28ES Sect-11.4 P-29ES Sect-11.4 P-30ES Sect-11.4 P-31ES Sect-11.4 P-32ES Sect-11.4 P-33ES Sect-11.4 P-34ES Sect-11.4 P-35ES Sect-11.4 P-36ES Sect-11.4 P-37ES Sect-11.4 P-38ES Sect-11.4 P-39ES Sect-11.4 P-40ES Sect-11.4 P-41ES Sect-11.4 P-42ES Sect-11.4 P-43ES Sect-11.4 P-44ES Sect-11.4 P-45ES Sect-11.4 P-46ES Sect-11.4 P-47ES Sect-11.4 P-48ES Sect-11.4 P-49ES Sect-11.4 P-50ES Sect-11.4 P-51ES Sect-11.5 P-1TY Sect-11.5 P-2TY Sect-11.5 P-3TY Sect-11.5 P-4TY Sect-11.5 P-5TY Sect-11.5 P-1ES Sect-11.5 P-2ES Sect-11.5 P-3ES Sect-11.5 P-4ES Sect-11.5 P-5ES Sect-11.5 P-6ES Sect-11.5 P-7ES Sect-11.5 P-8ES Sect-11.5 P-9ES Sect-11.5 P-10ES Sect-11.5 P-11ES Sect-11.5 P-12ES Sect-11.5 P-13ES Sect-11.5 P-14ES Sect-11.5 P-15ES Sect-11.5 P-16ES Sect-11.5 P-17ES Sect-11.5 P-18ES Sect-11.5 P-19ES Sect-11.5 P-20ES Sect-11.5 P-21ES Sect-11.5 P-22ES Sect-11.5 P-23ES Sect-11.5 P-24ES Sect-11.5 P-25ES Sect-11.5 P-26ES

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