   Chapter 9.1, Problem 33ES ### 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
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# Prove Theorem 9.1.1. (Let m be any integer and prove the theorem by mathematical induction on n.)

To determine

Proof of the given theorem by mathematical induction on n.

Explanation

Given information:

A theorem is given as, If m and n are integers and mn, then there are nm+1 integers from m to n inclusive

Calculation:

Let’s say p(m,n)=nm+1 which denotes the above formula.

Proof by induction:

The base case:

show that the statement holds for m=n=1.

p(m,n)=11+1p(m,n)=1

There is total 1 number between m=1,n=1.

Hence, base condition is proved.

Inductive step for m :

Show that if p(k,n) holds then p(k+1,n) also holds.

Since, p(k,n)=nk+1 holds,

p(k+1,n)=n(k+1)+1p(k+1,n)=nk+1−</

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