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Elements Of Modern Algebra

8th Edition

Gilbert, Linda, Jimmie

Publisher: Cengage Learning,

ISBN: 9781285463230

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Chapter

Section

Problem 1TFE:

True or False Label each of the following statements as either true or false. Two sets are equal if...

Problem 2TFE:

True or False
Label each of the following statements as either true or false.
2. If is a subset of ...

Problem 3TFE:

True or False
Label each of the following statements as either true or false.
3. The empty set is a...

Problem 4TFE:

True or False Label each of the following statements as either true or false. AA= for all sets A.

Problem 5TFE:

True or False Label each of the following statements as either true or false. AA=AA for all sets A.

Problem 6TFE:

True or False Label each of the following statements as either true or false. AA for all sets A.

Problem 9TFE:

True or False Label each of the following statements as either true or false. AB=CB implies A=C, for...

Problem 10TFE:

True or False Label each of the following statements as either true or false. AB=AC implies B=C, for...

Problem 1E:

For each set A, describe A by indicating a property that is a qualification for membership in A. a....

Problem 3E:

Decide whether or not each statement is true. (a) a{a,{a}} (b) {a}{a,{a}} (c) {a}{a,{a}} (d)...

Problem 4E:

4. Decide whether or not each of the following is true for all sets .
a. b.
c. d.
e. ...

Problem 5E:

Evaluate each of the following sets, where U={ 0,1,2,3,,10 }A={ 0,1,2,3,4,5 }B={ 0,2,4,6,8,10 }C={...

Problem 6E:

6. Determine whether each of the following is either , , , or , where is an arbitrary subset of the...

Problem 7E:

Write out the power set, (A), for each set A. a. A={ a } b. A={ 0,1 } c. A={ a,b,c } d. A={ 1,2,3,4...

Problem 10E:

10. Suppose the set has a .
a. How many elements does the power set have ?
b. If how many...

Problem 11E:

11. State the most general conditions on the subsets under which the given equality holds.
(a) ...

Problem 14E:

In Exercises 1435, prove each statement. ABAB

Problem 15E:

In Exercises 1435, prove each statement. (A)=A

Problem 18E:

In Exercises , prove each statement.
18.

Problem 19E:

In Exercises , prove each statement.
19.

Problem 20E:

In Exercises 1435, prove each statement. (AB)=AB

Problem 21E:

In Exercise 14-35, prove each statement.
21.

Problem 22E:

In Exercise 14-35, prove each statement. A(AB)=AB

Problem 23E:

In Exercises 14-35, prove each statement.
23.

Problem 24E:

In Exercise 14-35, prove each statement. A(AB)=A(AB)

Problem 27E:

In Exercise 14-35, prove each statement.
27.

Problem 28E:

In Exercise 14-35, prove each statement. A(BA)=

Problem 29E:

In Exercises 14-35, prove each statement.
29.

Problem 31E:

In Exercises 1435, prove each statement. (AB)(AB)=A

Problem 33E:

In Exercises , prove each statement.
33.

Problem 36E:

Prove or disprove that AB=AC implies B=C.

Problem 37E:

Prove or disprove that AB=AC implies B=C.

Problem 38E:

38. Prove or disprove that .

Problem 39E:

Prove or disprove that (AB)=(A)(B).

Problem 40E:

40. Prove or disprove that .

Show more chapters

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

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.

We offer sample solutions for Elements Of Modern Algebra homework problems. See examples below:

Label each of the following statements as either true or false. Every mapping on a nonempty set A is...Label each of the following statements as either true or false.
The notation mod is used to...Label each of the following statements as either true or false. Every homomorphism is an...True or False Label each of the following statements as either true or false. A p-group can be...True or False Label each of the following statements as either true or false. The field Q of...Label each of the following statements as either true or false. The only ideal of a ring R that...True or False
Label each of the following statements as either true or false.
There is a...

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