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Prove that if m is an integer, then ?x? +?m ? x? = m ?

Discrete Mathematics and Its Applications | 7th Edition | ISBN: 9780073383095 | Authors: Kenneth Rosen ISBN: 9780073383095 37

Solution for problem 23E 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 23E

Problem 23E

Prove that if m is an integer, then ⌊x⌋ +⌊m − x⌋ = m − 1unless x is an integer, in which case, it equals m.

 

Step-by-Step Solution:

Solution:

Step 1:

      In this problem we need to prove that if m is an integer , then

      unless  x is an integer , in which case , it equals to m.

   

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

                     

                   

   Example :  

                 

Example : {2.3} = 0.3

Case(1): If x is not an integer , then

             

                                     

                                       

                                       

                                        .

 Therefore , if x is not an integer then

                                   

Step 2 of 2

Chapter 2.SE, Problem 23E is Solved
Textbook: Discrete Mathematics and Its Applications
Edition: 7
Author: Kenneth Rosen
ISBN: 9780073383095

The answer to “Prove that if m is an integer, then ?x? +?m ? x? = m ? 1unless x is an integer, in which case, it equals m.” is broken down into a number of easy to follow steps, and 26 words. This full solution covers the following key subjects: Integer, Case, equals, prove, unless. 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. The full step-by-step solution to problem: 23E from chapter: 2.SE was answered by , our top Math solution expert on 06/21/17, 07:45AM. This textbook survival guide was created for the textbook: Discrete Mathematics and Its Applications, edition: 7. Since the solution to 23E from 2.SE chapter was answered, more than 420 students have viewed the full step-by-step answer.

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Prove that if m is an integer, then ?x? +?m ? x? = m ?