For which real numbers x and y is it true that ?x +y? = ?

Discrete Mathematics and Its Applications | 7th Edition | ISBN: 9780073383095 | Authors: Kenneth Rosen

ISBN: 9780073383095 37

Solution for problem 21E Chapter 2.SE

Discrete Mathematics and Its Applications | 7th Edition

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Problem 21E

For which real numbers x and y is it true that ⌈x +y⌉ = ⌈ x⌉ +⌊ y ⌋

Step-by-Step Solution:

Solution

Step 1:

In this problem we need to show that

is true for all real numbers x and y.

NOTE: The symbols for floor and ceiling are like the square brackets [ ] with the top or bottom part missing.

Example :

Given: x and y are real numbers.

Let us consider , and where a , b are integers and are real numbers such that .

So ,

Now

, since

, since a , b are integers.

Therefore ,

................(1)

Step 2 of 2

Chapter 2.SE, Problem 21E is Solved

Textbook: Discrete Mathematics and Its Applications

Edition: 7

Author: Kenneth Rosen

ISBN: 9780073383095

This textbook survival guide was created for the textbook: Discrete Mathematics and Its Applications, edition: 7. The answer to “For which real numbers x and y is it true that ?x +y? = ? x? +? y ?” is broken down into a number of easy to follow steps, and 19 words. The full step-by-step solution to problem: 21E from chapter: 2.SE was answered by , our top Math solution expert on 06/21/17, 07:45AM. This full solution covers the following key subjects: Numbers, real, true. This expansive textbook survival guide covers 101 chapters, and 4221 solutions. Discrete Mathematics and Its Applications was written by and is associated to the ISBN: 9780073383095. Since the solution to 21E from 2.SE chapter was answered, more than 297 students have viewed the full step-by-step answer.