TEST BANK FOR Mathematical Proofs: A Transition to Advanced Mathematics 4th Edition by Gary Chartrand, Albert Polimeni , Ping Zhang 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 bn



0.1 Learning Mathematics bn



0.2 What Others Have Said About Writing
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0.3 Mathematical Writing bn



0.4 Using Symbols bn



0.5 Writing Mathematical Expressions bn bn



0.6 Common Words and Phrases in Mathematics bn bn bn bn bn



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



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



1.5 Partitions of Sets bn bn



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 bn bn



2.4 Implications
2.5 More on Implications bn bn



2.6 Biconditionals
2.7 Tautologies and Contradictions bn bn



2.8 Logical Equivalence bn



2.9 Some Fundamental Properties of Logical Equivalence
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2.10 Quantified Statements bn



2.11 Characterizations Exercises for Chapter 2 bn bn bn bn




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



3.2 Direct Proofs bn



3.3 Proof by Contrapositive bn bn



3.4 Proof by Cases bn bn



3.5 Proof Evaluations bn



Exercises for Chapter
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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 bn bn bn



4.4 Proofs Involving Sets bn bn



4.5 Fundamental Properties of Set Operations bn bn bn bn



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 bn bn



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5.3 A Review of Three Proof Techniques
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5.4 Existence Proofs bn



5.5 Disproving Existence Statements Exercises for Chapter 5
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6. Mathematical Induction bn



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
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7.1 Reviewing Direct Proof and Proof by Contrapositive
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7.2 Reviewing Proof by Contradiction and Existence Proofs
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7.3 Reviewing Induction Proofs bn bn



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 bn bn



8.2 Revisiting Quantified Statements bn bn



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



9.1 Relations
9.2 Properties of Relations bn bn



9.3 Equivalence Relations bn



9.4 Properties of Equivalence Classes bn bn bn



9.5 Congruence Modulo n bn bn



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 bn bn bn



10.3 Bijective Functions bn



10.4 Composition of Functions bn bn



10.5 Inverse Functions bn bn



Exercises for Chapter 10
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11. Cardinalities of Sets bn bn



11.1 Numerically Equivalent Sets bn bn



11.2 Denumerable Sets bn



11.3 Uncountable Sets bn



11.4 Comparing Cardinalities of Sets bn bn bn



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 bn bn bn



12.2 The Division Algorithm
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12.3 Greatest Common Divisors bn bn



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12.4 The Euclidean Algorithm
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12.5 Relatively Prime Integers bn bn



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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