   Chapter 9.2, Problem 45ES ### 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 9.2.2 by mathematical induction.

To determine

To prove the below by mathematical induction.

“For any integer n with n;;1, the number of permutations of a set with n elements is n! .”

Explanation

Given information:

For any integer n with n;;1, the number of permutations of a set with n elements is n!.

Concept used:

Principle of mathematical induction is used to prove the mathematical statement.

Proof:

The statement of the theorem is

“For any integer n1 the number of permutations of a set with n elements is n! .”

We have to prove this result by mathematical induction.

The number of permutations of a set with 1 element is 1=1!.

Let n=2.

Then, the numbers of permutations are 2×1=2!

We assume that the result is true for n=k.

i.e., the number of permutations of a set with k elements are k!

We now prove that the result is true for n=k+1

Let the set contain k+1 elements

i

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