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# a) Explain why n div 7 equals the number of complete weeks ISBN: 9780073383095 37

## Solution for problem 2E Chapter 4.SE

Discrete Mathematics and Its Applications | 7th Edition

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Problem 2E

a) Explain why n div 7 equals the number of complete weeks in n days,________________b) Explain why n div 24 equals the number of complete days in n hours.

Step-by-Step Solution:

SolutionStep 1:Here in part (a) we need to explain why ndiv 7 equals the number of complete weeks in 7 days and in part (b) we have to explain why n div 24 equals the number of complete days in n hours.Step 2:(a)To determine the day of the week from numerical operations,sunday through saturday are represented as numbers which may corresponding to sunday being the first day of the week,be 1 to 7(or,zero rejecting whole sevens)respectively.This is achieved with arithmetic modulo 7.Modulo 7 is an operation that remainder of a number being divided by 7.Thus the number 7 is treated as 0,8as 1,9 as 2,18 as 4,27 and so on.The interpretation of this being that if sunday is signified as day 1,then after 7 days the next day is also sunday and 18 will be as day 4,which is wednesday since this falls three days after sunday.

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##### ISBN: 9780073383095

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