2 For the given binary operations *, determinewhether they are commutative and associative(a) on Zaxb6)7defiea-bon Q1defineon z, define axb = 2axbabti296.

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Answered: 2 For the given binary operations *,…

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter5: Rings, Integral Domains, And Fields

Section5.3: The Field Of Quotients Of An Integral Domain

Problem 5E

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Suppose that the check digit is computed as described in Example . Prove that transposition errors of adjacent digits will not be detected unless one of the digits is the check digit. Example Using Check Digits Many companies use check digits for security purposes or for error detection. For example, an the digit may be appended to a -bit identification number to obtain the -digit invoice number of the form where the th bit, , is the check digit, computed as . If congruence modulo is used, then the check digit for an identification number . Thus the complete correct invoice number would appear as . If the invoice number were used instead and checked, an error would be detected, since .
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2 For the given binary operations *, determine whether they are commutative and associative (a) on Z defre axb-a-b (6) on Q define axbabt, e) on zt, define axb = 296 ab > "