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Catalogue of discrete mathematics
Chapter 65438 +0 Propositional Logic

1. 1 Proposition and Conjunction

Basic concepts of the proposition 1. 1. 1

1. 1.2 propositional conjunction

1.2 Proposition formula and its translation

1.3 truth table and equivalent formula

Truth table of propositional formula of 1.3. 1

Equivalence of 1.3.2 propositional formula

1.4 tautology

1.5 paradigm

1.5. 1 disjunctive normal form and conjunctive normal form

1.5.2 Principal disjunctive normal form

1.5.3 Main conjunctive normal form

1.6 Full-function conjunction set

1.7 Duality and Implication

1.7. 1 double formula

1.7.2 implication formula

1.8 propositional logic reasoning theory

Chapter II Predicate Logic

2. 1 individual, predicate and quantifier

2. 1. 1 individual

2. 1.2 predicate

2. 1.3 quantifier

2.2 Predicate formula

2.2. 1 predicate formula

2.2.2 Limited argument and free argument

2.3 the equivalence and implication of predicate calculus

2.4 toe-in paradigm

2.5 Inference theory of predicate logic

Chapter III Collection

3. The basic concept of1

3. Representation of1.1set

3. 1.2 subset and set are equal.

3. 1.3 power set

3.2 Operation of equipment

3.3 Set identity

3.4 Coverage and division of sets

3.5 Cartesian product

Chapter 4 Binary Relationship

4. 1 binary relation and its representation

4. 1. 1 the concept of binary relation

4. Representation of binary relation of1.2

4.2 the operation of the relationship

4.2. Intersection, Union, Complement and Symmetry Difference Operations of1Binary Relation

4.2.2 Compound operation of binary relation

4.2. Inverse operation of ternary relation

4.3 the nature of the relationship

4.4 Relationship Closing Operation

4.5 Equivalence relation

4.6 Compatibility Relationship

4.7 ordering relationship

4.7. 1 poset relation and hasse diagram

4.7.2 Total Order Relationship and Good Order Relationship

Chapter V Functions

5. Basic concept of1function

5.2 Inverse Function and Composite Function

5.2. 1 inverse function

5.2.2 Composite functions

5.3 Cardinality of a set

5.3. 1 Set equipotential

5.3.2 Finite Sets and Infinite Sets

Cardinality of a set

5.3.4 Comparison of set cardinality

Chapter VI Algebraic System

6. Basic concepts of1algebraic system

6. 1. 1 operation

6. 1.2 algebraic system

6.2 Properties of Binary Operation

6.2. 1 Basic operation attributes

Special element

6.3 subalgebra and product algebra

Chapter VII Groups, Rings and Domains

7. 1 semigroup and uniqueness

7. 1. 1 wide groups and semigroups

7. 1.2 Uniqueness

7.2 Group and Abel Group

7.2. Definition and attributes of1group

Abel group

7.3 subgroups

7.3. 1 Subgroup Concept

7.3.2 Determination of grouping

7.3.3 Element Order and Its Attributes

7.4 Coset and Lagrange Theorem

7.5 Normal subgroup

7.6 Homomorphism and Isomorphism

7.6. Homomorphism and Isomorphism of1Algebraic System

7.6.2 Homomorphism and Isomorphism of Groups

7.7 Cyclic groups

7.8 permutation group

7.9 Rings and domains

7.9. Definition and Basic Properties of1Ring

7.9.2 Several Common Special Rings

Subring

7.9.4 areas

7.9.5 Homomorphism of Rings and Domains

Eighth Generation Zhangge and Boolean Algebra

8. 1 grid

8. The concept and properties of1.1lattice

8. 1.2 Sublattice and Lattice Homomorphism

8. 1.3 distributive lattice

8. 1.4 has a complement.

8.2 Boolean algebra

8.2. Concepts and properties of1Boolean algebra

8.2.2 Subalgebras and Homomorphisms of Boolean Algebras

8.2.3 Structure of Finite Boolean Algebra

Chapter 9 Graph Theory

9. Basic concepts of1graph

9. 1. 1 chart

9. Degree and Properties of1.2 Nodes

9. 1.3 Multigraph, Simple Graph, Complete Graph and Regular Graph

Isomorphism of 9. 1.4 graphs

9. 1.5 Complementary Graph, Subgraph and Generated Subgraph

9.2 Roads and Circuits

9.3 connected graph

9.3. 1 undirected connected graph

9.3.2 Directed Connected Graph

9.4 Matrix representation of graphics

9.5 Euler diagram and Hamilton diagram

euler graph

Hamilton diagram

9.6 Tree

9.6. 1 undirected tree

Spanning tree

9.6.3 Root Tree and Its Application

9.7 Bipartite Graph and Matching

9.7. 1 Parts Drawing

matching

9.8 floor plan

9.8. 1 Basic concept of planning

Euler formula

9.8.3 Dual Graph of Planar Graph

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