Answered: Let U = {10, 11, 13,14,15,16,17,20} be… | bartleby

Elements Of Modern Algebra

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter1: Fundamentals

Section1.1: Sets

Problem 10E

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Question

Let U = {10, 11, 13,14,15,16,17,20} be a universal set, and the ordering of elements of U has the elements in increasing order. A set A has bit string
representation 11100001. Select all of the following that are members of A.
0
0
17
15
11
13
10
14
20
16

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15. Let be a binary operation on the non empty set . Prove that if contains an identity element with respect to , the identity element is unique.
6. Determine whether each of the following is either , , , or , where is an arbitrary subset of the universal set . a. b. c. d. e. f. g. h. i. j. k. l. m. n.
4. Let be the relation “congruence modulo 5” defined on as follows: is congruent to modulo if and only if is a multiple of , and we write . a. Prove that “congruence modulo ” is an equivalence relation. b. List five members of each of the equivalence classes and .
In this exercise set, all variables are integers. 2. Follow the instructions in Exercise for the congruence classes modulo . 1. List the distinct congruence classes modulo , exhibiting at least three elements in each class.
Label each of the following statements as either true or false. If a nonempty set contains an upper bound, then a least upper bound must exist in .
Assume that is an associative binary operation on the non empty set A. Prove that a[ b(cd) ]=[ a(bc) ]d for all a,b,c, and d in A.
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 .
In this exercise set, all variables are integers. 1. List the distinct congruence classes modulo , exhibiting at least three elements in each class.

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