吴士珑的BLOG(Shilong Wu)

Part Two Set Algebra

Overview of Set Algebra

Chapter 1 Definition of Set Algebra

1.1   Definition of Set Algebra

1.2   Explanation of Operations

1.3   Conversion of Compound Operations

1.4   Equivalent Expression of Compound Operations

1.5    Proof of Equivalent Expression

1.6   Affirmative Law Theorem and Reasonable Constant υ

1.7   Negative Law Theorem

1.8   Axioms of Classical Set Theory Got From Set Algebra

Chapter 2 Equation Transformation Rules on Set Algebra

  2.1 Overview of Equation Transformation Rules on Set Algebra

  2.2 Proving Equation Transformation Rules on Set Algebra

  2.3 Basic Model of Set Equation

  2.4 Equation Transformation Rules of Compound Operations

 2.5 Proving Compound Equation Transformation Rules

  3.1 Overview of Simplification of Set Expression

  3.2 Proving Basic Formula of Simplification

  3.3 Examples of Simplification of Set Expressions

  4.1 Proving Equality of Set Expression

  4.2 Proving Set Laws

  5.1 Solving Method of Set Equation in General Form

  5.2 Normal Form of Set Equation

  5.3 Least Solution Theorem and Most Solution Theorem in Normal Equation

  5.4 Solving Normal Form of Set Equation

Chapter 6 Set Theorems of Compound Operations

  6.1 Overview of Set Theorems of Compound Operations

  6.2 Proving Set Theorems of Compound Operations

Chapter 7 Set Equations of Compound Operations

  7.1 Overview

  7.2 Solving Set Equation of no same variable

  7.3 Solving Set Equation Constituted by Premises of Set Complementary Complement law

7.4 Solving Set Equation Constituted by Premises of Equal Complement law

7.5 Solving Set Equation Constituted by One Premise and Conclusion of Set Equal Complement law

7.6 Solving Set Equation Constituted by One Premise and Conclusion of Set Equal Transferring law

7.7 Solving Set Equation Constituted by One Premise and Conclusion of Set Complementary Complement law

Chapter 8 Deduction of Set Laws Using Compound Operation

8.1 Overview of Set Laws

8.2 Explanation of Set Laws

8.3 Proving Set Laws Using Compound Operation