   Chapter 11.5, Problem 7ES ### 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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# Suppose bot and top are positive integers with b o t ≤ t o p . Consider the array a [ b o t ] ,   a [ b o t + 1 ] ,   … ,   a [ t o p ] .a. How many elements are in this array?b. Show that lithe number of elements in the array is odd, then the quantity b o t + t o p is even.c. Show that if the number of elements in the array is even, then the quantity b o t + t o p is odd.

To determine

(a)

To find:

The number of elements in the array.

Explanation

Given information:

Suppose bot and topare positive integers with bottop.

The array is a[bot],a[bot+1],...,a[top].

Theorem used:

Number of elements in a list theorem: There are (nm+1) integers from m to n inclusive, if m and n are integers such that mn.

Calculation:

The array is a[bot],a[bot+1],...,a[top]

To determine

(b)

To prove:

If the number of elements in the array is odd, then the quantity bot+top is even.

To determine

(c)

To prove:

If the number of elements in the array is even, then the quantity bot+top is odd.

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