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Contents
Part ¢ñMathematical Logic
Chapter 1Propositional Logic
1.1Propositions and Connectives
1.2Propositional Formula and Translation
1.3Truth Tables and Equivalent Formulas
1.4Tautology and Implication
1.5Duality and Normal Form
1.6The Reasoning Theory of Propositional Calculus
1.7Application of Propositional Logic
Exercises
Chapter 2Predicate Logic
2.1Predicate and Quantifier
2.2Predicate Formula and Translation
2.3Constraints on Variables
2.4Equivalence and Implication of Predicate Calculus
2.5Prenex Normal Forms
2.6Inference Theory of Predicate Calculus
2.7Application of Predicate Logic
Exercises
Part ¢òSet Theory
Chapter 3Set and Relation
3.1The Concept and Representation of the Set
3.2Operation of Set
3.3Inclusion Exclusion Principle
3.4Ordered Pair and Cartesian Product
3.5Relation and Its Nature
3.6Inverse and Compound Relations
3.7Closure Operations
3.8Equivalence Relation and Compatible Relation
3.9Partial Order Relation
3.10Application of Set and Relation
Exercises
Chapter 4Function
4.1The Concept and Representation of Function
4.2Inverse Function and Compound Function
4.3The Concept of Characteristic Function and Fuzzy Subset
4.4Common Functions
ContentsĿ¼Exercises
Part ¢óThe Algebraic Structure
Chapter 5Algebra System
5.1The Introduction of Algebraic Systems
5.2Operations and Properties of Algebraic Systems
5.3Homomorphism and Isomorphism of Algebraic Systems
5.4Congruence and Quotient Algebra
5.5Product Algebra
Exercises
Chapter 6Group
6.1Semigroup
6.2Group and Subgroup
6.3Homomorphism and Isomorphism of Groups
6.4Abelian Groups and Cyclic Groups
Exercises
Chapter 7Lattice and Boolean Algebra
7.1The Concept and Properties of Lattice
7.2Distributive Lattice
7.3Complemented Lattice
7.4Boolean Algebra
7.5Boolean Expression
ExercisesPart ¢ôGraph TheoryChapter 8Basic Concepts of Graphs
8.1Concept of Graph
8.2Subgraph and Isomorphic Graph
8.3Path and Loop
8.4Matrix Representation of Graph
Exercises
Chapter 9Euler Graph and Hamiltonian Graph
9.1Euler Graph
9.2Hamiltonian Graph
9.3Application of Euler Graph and Hamiltonian Graph
Exercises
Chapter 10Planar Graph
10.1Basic Concepts of the Planar Graph
10.2Euler Formula and Judgment of Planar Graph
10.3Dual Graph and Properties
10.4Application of the Planar Graph
Exercises
Chapter 11Tree
11.1The Concept and Properties of Trees
11.2Spanning Tree
11.3Directed Tree
11.4Root Trees and Their Applications
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