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Get Full Access to Discrete Mathematics And Its Applications - 7 Edition - Chapter 2.3 - Problem 52e
Get Full Access to Discrete Mathematics And Its Applications - 7 Edition - Chapter 2.3 - Problem 52e

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# Solved: Show that if x is a real number and n is an ISBN: 9780073383095 37

## Solution for problem 52E Chapter 2.3

Discrete Mathematics and Its Applications | 7th Edition

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Problem 52E

Problem 52E

Show that if x is a real number and n is an integer, then Step-by-Step Solution:
Step 1 of 3

Solution:

Step1

Given that

We have to show that if x is a real number and n is an integer, then  Step2 Suppose n<x ------------(1)

By using definition of Ceiling function “ it assigns to the real number y the smallest integer that is greater than or equal to y.”

Therefore, -----------------(2)

From (1) and (2) we get Hence, if n x then ----------------(3)

Step3

Suppose By using definition of  Ceiling Function If then This shows

If then

n< x  -----------------(4)

From (3) and (4) we get Step4 Suppose x<n ---------(5)

By using definition of floor function, “ The Floor Function assigns to the real number y the largest integer that is less than or equal to y.”

Therefore, -------------------(6)

From (5) and (6) we get If ----------------(7)

Step3

Suppose Using Floor Function definition If then This shows that

If then --------(8)

From (7) and (8) we get Step 2 of 3

Step 3 of 3

##### ISBN: 9780073383095

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