SOLUTION MANUAL FOR Mathematical Proofs: A Transition to Advanced Mathematics 4th Edition by Gary Chartrand, Albert Polimeni ISBN:978-0134746753 COMPLETE GUIDE ALL CHAPTERS COVERED 100% VERIFIED A+ GRADE ASSURED!!!!!!NEW LATEST UPDATE!!!!!!

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Table of Contents
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0. Communicating Mathematics br



0.1 Learning Mathematics br



0.2 What Others Have Said About Writing
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0.3 Mathematical Writing br



0.4 Using Symbols br



0.5 Writing Mathematical Expressions br br



0.6 Common Words and Phrases in Mathematics br br br br br



0.7 Some Closing Comments About Writing
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1. Sets
1.1 Describing a Set br br



1.2 Subsets
1.3 Set Operations
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1.4 Indexed Collections of Sets br br br



1.5 Partitions of Sets br br



1.6 Cartesian Products of Sets Exercises for Chapter 1
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2. Logic
2.1 Statements
2.2 Negations
2.3 Disjunctions and Conjunctions br br



2.4 Implications
2.5 More on Implications br br



2.6 Biconditionals
2.7 Tautologies and Contradictions br br



2.8 Logical Equivalence br



2.9 Some Fundamental Properties of Logical Equivalence
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2.10 Quantified Statements br



2.11 Characterizations Exercises for Chapter 2 br br br br




3. Direct Proof and Proof by Contrapositive
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3.1 Trivial and Vacuous Proofs br br br



3.2 Direct Proofs br



3.3 Proof by Contrapositive br br



3.4 Proof by Cases br br



3.5 Proof Evaluations br



Exercises for Chapter 3
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4. More on Direct Proof and Proof by Contrapositive
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4.1 Proofs Involving Divisibility of Integers
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4.2 Proofs Involving Congruence of Integers
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4.3 Proofs Involving Real Numbers br br br



4.4 Proofs Involving Sets br br



4.5 Fundamental Properties of Set Operations br br br br



4.6 Proofs Involving Cartesian Products of Sets Exercises for Chapter 4
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5. Existence and Proof by Contradiction
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5.1 Counterexamples
5.2 Proof by Contradiction br br



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5.3 A Review of Three Proof Techniques
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5.4 Existence Proofs br



5.5 Disproving Existence Statements Exercises for Chapter 5 br br br br br br




6. Mathematical Induction br



6.1 The Principle of Mathematical Induction
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6.2 A More General Principle of Mathematical Induction
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6.3 The Strong Principle of Mathematical Induction
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6.4 Proof by Minimum Counterexample Exercises for Chapter 6
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7. Reviewing Proof Techniques br br



7.1 Reviewing Direct Proof and Proof by Contrapositive br br br br br br



7.2 Reviewing Proof by Contradiction and Existence Proofs br br br br br br



7.3 Reviewing Induction Proofs br br



7.4 Reviewing Evaluations of Proposed Proofs Exercises for Chapter 7
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8. Prove or Disprove
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8.1 Conjectures in Mathematics br br



8.2 Revisiting Quantified Statements br br



8.3 Testing Statements Exercises for Chapter 8
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9. Equivalence Relations br



9.1 Relations
9.2 Properties of Relations br br



9.3 Equivalence Relations br



9.4 Properties of Equivalence Classes br br br



9.5 Congruence Modulo n br br



9.6 The Integers Modulo n Exercises for Chapter 9
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10. Functions
10.1 The Definition of Function
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10.2 One-to-one and Onto Functions br br br



10.3 Bijective Functions br



10.4 Composition of Functions br br



10.5 Inverse Functions br br



Exercises for Chapter 10
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11. Cardinalities of Sets br br



11.1 Numerically Equivalent Sets br br



11.2 Denumerable Sets br



11.3 Uncountable Sets br



11.4 Comparing Cardinalities of Sets br br br



11.5 The Schroder-Bernstein Theorem¨ Exercises for Chapter 11
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12. Proofs in Number Theory
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12.1 Divisibility Properties of Integers br br br



12.2 The Division Algorithm
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12.3 Greatest Common Divisors br br



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12.4 The Euclidean Algorithm
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12.5 Relatively Prime Integers br br



12.6 The Fundamental Theorem of Arithmetic
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12.7 Concepts Involving Sums of Divisors Exercises for Chapter 12
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13. Proofs in Combinatorics
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13.1 The Multiplication and Addition Principles
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13.2 The Principle of Inclusion-Exclusion
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13.3 The Pigeonhole Principle
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13.4 Permutations and Combinations br br



13.5 The Pascal Triangle
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13.6 The Binomial Theorem
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13.7 Permutations and Combinations with Repetition Exercises for Chapter 13br br br br br br br br




14. Proofs in Calculus
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14.1 Limits of Sequences br br



14.2 Infinite Series br



14.3 Limits of Functions br br



14.4 Fundamental Properties of Limits of Functions br br br br br



14.5 Continuity
14.6 Differentiability Ex br



ercises for Chapter 14
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15. Proofs in Group Theory
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15.1 Binary Operations br



15.2 Groups
15.3 Permutation Groups br



15.4 Fundamental Properties of Groups br br br



15.5 Subgroups
15.6 Isomorphic Groups Exercises for Chapter 15 br br br br br




16. Proofs in Ring Theory (Online)
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16.1 Rings
16.2 Elementary Properties of Rings br br br



16.3 Subrings
16.4 Integral Domains 16.5 Fields br br br br



Exercises for Chapter 16
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17. Proofs in Linear Algebra (Online)
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17.1 Properties of Vectors in 3-Space br br br br



17.2 Vector Spaces br



17.3 Matrices
17.4 Some Properties of Vector Spaces
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17.5 Subspaces
17.6 Spans of Vectors br br



17.7 Linear Dependence and Independence
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17.8 Linear Transformations br



17.9 Properties of Linear Transformations br br br br



Exercises for Chapter 17
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18. Proofs with Real and Complex Numbers (Online)
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18.1 The Real Numbers as an Ordered Field
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18.2 The Real Numbers and the Completeness Axiom
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18.3 Open and Closed Sets of Real Numbers
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18.4 Compact Sets of Real Numbers br br br br



18.5 Complex Numbers br



18.6 De Moivre’s Theorem and Euler’s Formula Exercises for Chapter 18
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