Elements Of Modern Algebra8th EditionGilbert, Linda, Jimmie Publisher: Cengage Learning,ISBN: 9781285463230
Elements Of Modern Algebra
Solutions for Elements Of Modern Algebra
Problem 1TFE:
Label each of the following statements as either true or false.
1. , for every nonempty set A.
Problem 2TFE:
Label each of the following statements as either true or false.
2. for all nonempty sets A and B.
Problem 3TFE:
Label each of the following statements as either true or false.
3. Let where A and B are nonempty....Problem 4TFE:
Label each of the following statements as either true or false. Let f:AB where A and B are nonempty....Problem 5TFE:
Label each of the following statements as either true or false. Let f:AB. Then f(A)=B for all...Problem 6TFE:
True or False
Label each of the following statements as either true or false.
6. Every bijection is...Problem 7TFE:
Label each of the following statements as either true or false. A mapping is onto if and only if its...Problem 8TFE:
Label each of the following statements as either true or false.
8. Let and . Then for every in .
Problem 9TFE:
Label each of the following statements as either true or false.
9. Composition of mappings is an...Problem 2E:
For each of the following mapping, state the domain, the codomain, and the range, where f:EZ....Problem 4E:
For each of the following mappings f:ZZ, determine whether the mapping is onto and whether it is...Problem 5E:
5. For each of the following mappings, determine whether the mapping is onto and whether it is...Problem 6E:
6. For the given subsets and of Z, let and determine whether is onto and whether it is...Problem 7E:
7. For the given subsets and of Z, let and determine whether is onto and whether it is...Problem 8E:
8. For the given subsets and of Z, let and determine whether is onto and whether it is...Problem 9E:
For the given subsets A and B of Z, let f(x)=2x and determine whether f:AB is onto and whether it is...Problem 10E:
For each of the following parts, give an example of a mapping from E to E that satisfies the given...Problem 11E:
For the given f:ZZ, decide whether f is onto and whether it is one-to-one. Prove that your decisions...Problem 12E:
12. Let and . For the given , decide whether is onto and whether it is one-to-one. Prove that your...Problem 13E:
13. For the given decide whether is onto and whether it is one-to-one. Prove that your decisions...Problem 15E:
15. a. Show that the mapping given in Example 2 is neither onto nor one-to-one.
b. For this mapping...Problem 18E:
18. Let and be defined as follows. In each case, compute for arbitrary .
a.
b.
c.
d.
e.
Problem 21E:
In Exercises 20-22, Suppose and are positive integers, is a set with elements, and is a set...Problem 23E:
Let a and b be constant integers with a0, and let the mapping f:ZZ be defined by f(x)=ax+b. Prove...Problem 24E:
24. Let, where and are nonempty.
Prove that for all subsets and of.
Prove that for all subsets...Problem 25E:
25. Let, where and are non empty, and let and be subsets of .
Prove that.
Prove that.
Prove...Problem 26E:
26. Let and. Prove that for any subset of T of .
Browse All Chapters of This Textbook
Chapter 1.1 - SetsChapter 1.2 - MappingsChapter 1.3 - Properties Of Composite Mappings (optional)Chapter 1.4 - Binary OperationsChapter 1.5 - Permutations And InversesChapter 1.6 - MatricesChapter 1.7 - RelationsChapter 2.1 - Postulates For The Integers (optional)Chapter 2.2 - Mathematical InductionChapter 2.3 - Divisibility
Chapter 2.4 - Prime Factors And Greatest Common DivisorChapter 2.5 - Congruence Of IntegersChapter 2.6 - Congruence ClassesChapter 2.7 - Introduction To Coding Theory (optional)Chapter 2.8 - Introduction To Cryptography (optional)Chapter 3.1 - Definition Of A GroupChapter 3.2 - Properties Of Group ElementsChapter 3.3 - SubgroupsChapter 3.4 - Cyclic GroupsChapter 3.5 - IsomorphismsChapter 3.6 - HomomorphismsChapter 4.1 - Finite Permutation GroupsChapter 4.2 - Cayley’s TheoremChapter 4.3 - Permutation Groups In Science And Art (optional)Chapter 4.4 - Cosets Of A SubgroupChapter 4.5 - Normal SubgroupsChapter 4.6 - Quotient GroupsChapter 4.7 - Direct Sums (optional)Chapter 4.8 - Some Results On Finite Abelian Groups (optional)Chapter 5.1 - Definition Of A RingChapter 5.2 - Integral Domains And FieldsChapter 5.3 - The Field Of Quotients Of An Integral DomainChapter 5.4 - Ordered Integral DomainsChapter 6.1 - Ideals And Quotient RingsChapter 6.2 - Ring HomomorphismsChapter 6.3 - The Characteristic Of A RingChapter 6.4 - Maximal Ideals (optional)Chapter 7.1 - The Field Of Real NumbersChapter 7.2 - Complex Numbers And QuaternionsChapter 7.3 - De Moivre’s Theorem And Roots Of Complex NumbersChapter 8.1 - Polynomials Over A RingChapter 8.2 - Divisibility And Greatest Common DivisorChapter 8.3 - Factorization In F [x]Chapter 8.4 - Zeros Of A PolynomialChapter 8.5 - Solution Of Cubic And Quartic Equations By Formulas (optional)Chapter 8.6 - Algebraic Extensions Of A Field
Book Details
ELEMENTS OF MODERN ALGEBRA, Eighth Edition, with its user-friendly format, provides you with the tools you need to succeed in abstract algebra and develop mathematical maturity as a bridge to higher-level mathematics courses. Strategy boxes give you guidance and explanations about techniques and enable you to become more proficient at constructing proofs. A summary of key words and phrases at the end of each chapter help you master the material. A reference section, symbolic marginal notes, an appendix, and numerous examples help you develop your problem-solving skills.
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EBK ELEMENTS OF MODERN ALGEBRA
8th Edition
ISBN: 9780100475755
ELEMENTS OF MODERN ALGEBRA
8th Edition
ISBN: 9780357671139
EBK ELEMENTS OF MODERN ALGEBRA
8th Edition
ISBN: 8220100475757
Elements Of Modern Algebra
8th Edition
ISBN: 9781285965918
Elements of Modern Algebra
5th Edition
ISBN: 9780534373511
Elements of Modern Algebra
6th Edition
ISBN: 9780534402648
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