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

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.

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