   Chapter 11.2, Problem 46ES ### 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
1 views

# 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 nm1 for every integer m1, for any integer n1, using the mathematical induction.

Explanation

Given information:

The integers n and m are given as n1 and m1.

Proof:

First, let’s consider when m=1 ,

nm=1=n1=n

Because n1 is a given condition, nm1 is true for m=1.

Then, let’s assume that the result is true for m=p where p1.

nm=p=np1

Now, for m=p+1 ,

nm=p+1

To determine

(b)

To prove:

That nrns for all integer r and s where rs for any integer n1.

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