Explanation Given : [ T h e c o n t r a p o s i t i v e i s : F o r a l l int e g e r s n , i f 5 / n t h e n 5 / n 2 . ] Suppose n is any integer such that (a). [ we must show that ( b ) . ] By definition of divisibility, n =(c) for some integer k . By substitution, n 2 =(d)= 5 ( 5 k 2 ) . But 5 k 2 is an integer because it is a product of integers. Hence n 2 = 5 . (an integer), and so (e) [ as was to be s h o w n ]

11th Edition

ISBN: 9781133417071

Author: EPP

Publisher: CENGAGE LEARNING - CONSIGNMENT

See similar textbooks

Videos

Question

Chapter 4.5, Problem 18ES

To determine

Tofind:Fill in the blanks in the following proof by contraposition that for all integers n , if 5 is not divide n2 then 5 is not divide n .

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 4.5, Problem 17ES

Chapter 4.5, Problem 19ES

Chapter 4 Solutions

EBK DISCRETE MATHEMATICS: INTRODUCTION

Ch. 4.1 - Prob. 1ES Ch. 4.1 - Prob. 2ES Ch. 4.1 - Prob. 3ES Ch. 4.1 - Prob. 4ES Ch. 4.1 - Prob. 5ES Ch. 4.1 - Prob. 6ES Ch. 4.1 - Prob. 7ES Ch. 4.1 - Prob. 8ES Ch. 4.1 - Prob. 9ES Ch. 4.1 - Prob. 10ES

Ch. 4.1 - Prob. 11ES Ch. 4.1 - Prob. 12ES Ch. 4.1 - Prob. 13ES Ch. 4.1 - Prob. 14ES Ch. 4.1 - Prob. 15ES Ch. 4.1 - Prob. 16ES Ch. 4.1 - Prob. 17ES Ch. 4.1 - Prob. 18ES Ch. 4.1 - Prob. 19ES Ch. 4.1 - Prob. 20ES Ch. 4.1 - Prob. 21ES Ch. 4.1 - Prob. 22ES Ch. 4.1 - Prob. 23ES Ch. 4.1 - Prob. 24ES Ch. 4.1 - Prob. 25ES Ch. 4.1 - Prob. 26ES Ch. 4.1 - Prob. 27ES Ch. 4.1 - Prob. 28ES Ch. 4.1 - Prob. 29ES Ch. 4.1 - Prob. 30ES Ch. 4.1 - Prob. 31ES Ch. 4.1 - Prob. 32ES Ch. 4.1 - Prob. 33ES Ch. 4.1 - Prob. 34ES Ch. 4.1 - Prob. 35ES Ch. 4.1 - Prob. 36ES Ch. 4.1 - Prob. 37ES Ch. 4.1 - Prob. 38ES Ch. 4.1 - Prob. 39ES Ch. 4.1 - Prob. 40ES Ch. 4.1 - Prob. 41ES Ch. 4.1 - Prob. 42ES Ch. 4.1 - Prob. 43ES Ch. 4.1 - Prob. 44ES Ch. 4.1 - Prob. 45ES Ch. 4.1 - Prob. 46ES Ch. 4.1 - Prob. 47ES Ch. 4.1 - Prob. 48ES Ch. 4.1 - Prob. 49ES Ch. 4.1 - Prob. 50ES Ch. 4.1 - Prob. 51ES Ch. 4.1 - Prob. 52ES Ch. 4.1 - Prob. 53ES Ch. 4.1 - Prob. 54ES Ch. 4.1 - Prob. 55ES Ch. 4.1 - Prob. 56ES Ch. 4.1 - Prob. 57ES Ch. 4.1 - Prob. 58ES Ch. 4.1 - Prob. 59ES Ch. 4.1 - Prob. 60ES Ch. 4.1 - Prob. 61ES Ch. 4.1 - Prob. 62ES Ch. 4.1 - Prob. 63ES Ch. 4.2 - Prob. 1ES Ch. 4.2 - Prob. 2ES Ch. 4.2 - Prob. 3ES Ch. 4.2 - Prob. 4ES Ch. 4.2 - Prob. 5ES Ch. 4.2 - Prob. 6ES Ch. 4.2 - Prob. 7ES Ch. 4.2 - Prob. 8ES Ch. 4.2 - Prob. 9ES Ch. 4.2 - Prob. 10ES Ch. 4.2 - Prob. 11ES Ch. 4.2 - Prob. 12ES Ch. 4.2 - Prob. 13ES Ch. 4.2 - Prob. 14ES Ch. 4.2 - Prob. 15ES Ch. 4.2 - Prob. 16ES Ch. 4.2 - Prob. 17ES Ch. 4.2 - Prob. 18ES Ch. 4.2 - Prob. 19ES Ch. 4.2 - Prob. 20ES Ch. 4.2 - Prob. 21ES Ch. 4.2 - Prob. 22ES Ch. 4.2 - Prob. 23ES Ch. 4.2 - Prob. 24ES Ch. 4.2 - Prob. 25ES Ch. 4.2 - Prob. 26ES Ch. 4.2 - Prob. 27ES Ch. 4.2 - Prob. 28ES Ch. 4.2 - Prob. 29ES Ch. 4.2 - Prob. 30ES Ch. 4.2 - Prob. 31ES Ch. 4.2 - Prob. 32ES Ch. 4.2 - Prob. 33ES Ch. 4.2 - Prob. 34ES Ch. 4.2 - Prob. 35ES Ch. 4.2 - Prob. 36ES Ch. 4.2 - Prob. 37ES Ch. 4.2 - Prob. 38ES Ch. 4.2 - Prob. 39ES Ch. 4.3 - Prob. 1ES Ch. 4.3 - Prob. 2ES Ch. 4.3 - Prob. 3ES Ch. 4.3 - Prob. 4ES Ch. 4.3 - Prob. 5ES Ch. 4.3 - Prob. 6ES Ch. 4.3 - Prob. 7ES Ch. 4.3 - Prob. 8ES Ch. 4.3 - Prob. 9ES Ch. 4.3 - Prob. 10ES Ch. 4.3 - Prob. 11ES Ch. 4.3 - Prob. 12ES Ch. 4.3 - Prob. 13ES Ch. 4.3 - Prob. 14ES Ch. 4.3 - Prob. 15ES Ch. 4.3 - Prob. 16ES Ch. 4.3 - Prob. 17ES Ch. 4.3 - Prob. 18ES Ch. 4.3 - Prob. 19ES Ch. 4.3 - Prob. 20ES Ch. 4.3 - Prob. 21ES Ch. 4.3 - Prob. 22ES Ch. 4.3 - Prob. 23ES Ch. 4.3 - Prob. 24ES Ch. 4.3 - Prob. 25ES Ch. 4.3 - Prob. 26ES Ch. 4.3 - Prob. 27ES Ch. 4.3 - Prob. 28ES Ch. 4.3 - Prob. 29ES Ch. 4.3 - Prob. 30ES Ch. 4.3 - Prob. 31ES Ch. 4.3 - Prob. 32ES Ch. 4.3 - Prob. 33ES Ch. 4.3 - Prob. 34ES Ch. 4.3 - Prob. 35ES Ch. 4.3 - Prob. 36ES Ch. 4.3 - Prob. 37ES Ch. 4.3 - Prob. 38ES Ch. 4.3 - Prob. 39ES Ch. 4.3 - Prob. 40ES Ch. 4.3 - Prob. 41ES Ch. 4.3 - Prob. 42ES Ch. 4.3 - Prob. 43ES Ch. 4.3 - Prob. 44ES Ch. 4.3 - Prob. 45ES Ch. 4.3 - Prob. 46ES Ch. 4.3 - Prob. 47ES Ch. 4.3 - Prob. 48ES Ch. 4.3 - Prob. 49ES Ch. 4.4 - Prob. 1ES Ch. 4.4 - Prob. 2ES Ch. 4.4 - Prob. 3ES Ch. 4.4 - Prob. 4ES Ch. 4.4 - Prob. 5ES Ch. 4.4 - Prob. 6ES Ch. 4.4 - Prob. 7ES Ch. 4.4 - Prob. 8ES Ch. 4.4 - Prob. 9ES Ch. 4.4 - Prob. 10ES Ch. 4.4 - Prob. 11ES Ch. 4.4 - Prob. 12ES Ch. 4.4 - Prob. 13ES Ch. 4.4 - Prob. 14ES Ch. 4.4 - Prob. 15ES Ch. 4.4 - Prob. 16ES Ch. 4.4 - Prob. 17ES Ch. 4.4 - Prob. 18ES Ch. 4.4 - Prob. 19ES Ch. 4.4 - Prob. 20ES Ch. 4.4 - Prob. 21ES Ch. 4.4 - Prob. 22ES Ch. 4.4 - Prob. 23ES Ch. 4.4 - Prob. 24ES Ch. 4.4 - Prob. 25ES Ch. 4.4 - Prob. 26ES Ch. 4.4 - Prob. 27ES Ch. 4.4 - Prob. 28ES Ch. 4.4 - Prob. 29ES Ch. 4.4 - Prob. 30ES Ch. 4.4 - Prob. 31ES Ch. 4.4 - Prob. 32ES Ch. 4.4 - Prob. 33ES Ch. 4.4 - Prob. 34ES Ch. 4.4 - Prob. 35ES Ch. 4.4 - Prob. 36ES Ch. 4.4 - Prob. 37ES Ch. 4.4 - Prob. 38ES Ch. 4.4 - Prob. 39ES Ch. 4.4 - Prob. 40ES Ch. 4.4 - Prob. 41ES Ch. 4.4 - Prob. 42ES Ch. 4.4 - Prob. 43ES Ch. 4.4 - Prob. 44ES Ch. 4.4 - Prob. 45ES Ch. 4.4 - Prob. 46ES Ch. 4.5 - Prob. 1ES Ch. 4.5 - Prob. 2ES Ch. 4.5 - Prob. 3ES Ch. 4.5 - Prob. 4ES Ch. 4.5 - Prob. 5ES Ch. 4.5 - Prob. 6ES Ch. 4.5 - Prob. 7ES Ch. 4.5 - Prob. 8ES Ch. 4.5 - Prob. 9ES Ch. 4.5 - Prob. 10ES Ch. 4.5 - Prob. 11ES Ch. 4.5 - Prob. 12ES Ch. 4.5 - Prob. 13ES Ch. 4.5 - Prob. 14ES Ch. 4.5 - Prob. 15ES Ch. 4.5 - Prob. 16ES Ch. 4.5 - Prob. 17ES Ch. 4.5 - Prob. 18ES Ch. 4.5 - Prob. 19ES Ch. 4.5 - Prob. 20ES Ch. 4.5 - Prob. 21ES Ch. 4.5 - Prob. 22ES Ch. 4.5 - Prob. 23ES Ch. 4.5 - Prob. 24ES Ch. 4.5 - Prob. 25ES Ch. 4.5 - Prob. 26ES Ch. 4.5 - Prob. 27ES Ch. 4.5 - Prob. 28ES Ch. 4.5 - Prob. 29ES Ch. 4.5 - Prob. 30ES Ch. 4.5 - Prob. 31ES Ch. 4.5 - Prob. 32ES Ch. 4.5 - Prob. 33ES Ch. 4.5 - Prob. 34ES Ch. 4.5 - Prob. 35ES Ch. 4.6 - Prob. 1ES Ch. 4.6 - Prob. 2ES Ch. 4.6 - Prob. 3ES Ch. 4.6 - Prob. 4ES Ch. 4.6 - Prob. 5ES Ch. 4.6 - Prob. 6ES Ch. 4.6 - Prob. 7ES Ch. 4.6 - Prob. 8ES Ch. 4.6 - Prob. 9ES Ch. 4.6 - Prob. 10ES Ch. 4.6 - Prob. 11ES Ch. 4.6 - Prob. 12ES Ch. 4.6 - Prob. 13ES Ch. 4.6 - Prob. 14ES Ch. 4.6 - Prob. 15ES Ch. 4.6 - Prob. 16ES Ch. 4.6 - Prob. 17ES Ch. 4.6 - Prob. 18ES Ch. 4.6 - Prob. 19ES Ch. 4.6 - Prob. 20ES Ch. 4.6 - Prob. 21ES Ch. 4.6 - Prob. 22ES Ch. 4.6 - Prob. 23ES Ch. 4.6 - Prob. 24ES Ch. 4.6 - Prob. 25ES Ch. 4.6 - Prob. 26ES Ch. 4.6 - Prob. 27ES Ch. 4.6 - Prob. 28ES Ch. 4.6 - Prob. 29ES Ch. 4.6 - Prob. 30ES Ch. 4.6 - Prob. 31ES Ch. 4.6 - Prob. 32ES Ch. 4.6 - Prob. 33ES Ch. 4.6 - Prob. 34ES Ch. 4.6 - Prob. 35ES

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, subject and related others by exploring similar questions and additional content below.

Tofind:Fill in the blanks in the following proof by contraposition that for all integers n , if 5 is not divide n 2 then 5 is not divide n .

Solution Summary: The author explains that 5 is not divide n2 for all integers.

Videos

Tofind:Fill in the blanks in the following proof by contraposition that for all integers n , if 5 is not divide n2 then 5 is not divide n .

Want to see the full answer?

Chapter 4 Solutions