1ABLet Define* be a binary operation on Z such that a*b = a + 3b-1for a, b e Z. Which statement best describes problem?Associative (No), commutative (No), identity (No), zero (No)Associative (Yes), commutative (Yes), identity (No), zero (No)Associative (Yes), commutative (No), identity (Yes), zero (No)Associative (Yes), commutative (No), identity (No), zero (Yes)Associative (No), commutative (No), identity (No), zero (Yes)...

Answered: Image /qna-images/answer/001f96de-42db-4018-8f39-43164b33b143.jpg

Answered: A Associative (No), commutative (No),…

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter1: Fundamentals

Section1.4: Binary Operations

Problem 14E: Assume that is a binary operation on a non empty set A, and suppose that is both commutative and...

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Similar questions

Assume that is a binary operation on a non empty set A, and suppose that is both commutative and associative. Use the definitions of the commutative and associative properties to show that [ (ab)c ]d=(dc)(ab) for all a,b,c and d in A.
Prove that the multiplication defined 5.24 is a binary operation on Lemma 5.24 Addition and Multiplication in The following rules define binary operations on Addition in is defined by and multiplication in is defined by
Write out the addition and multiplication tables for 4.
In each part following, a rule that determines a binary operation on the set of all integers is given. Determine in each case whether the operation is commutative or associative and whether there is an identity element. Also find the inverse of each invertible element. b. d. f. h. j. l. for n. for
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 .
True or False Label each of the following statements as either true or false. 7. Any binary operation defined on a set containing a single element is commutative and associative.
5. Let be the relation “congruence modulo ” defined on as follows: is congruent to modulo if and only if is a multiple of , we write . a. Prove that “congruence modulo ” is an equivalence relation. b. List five members of each of the equivalence classes and .

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