Lecture 1. Set Calculus 1.1.Concept of a Set 1.2.Operations on Sets 1.3.The Concepts of Partition and Cover of a Set Lecture 2. Cartesian Product of Sets. Relations on Sets 2.1.Cartesian Product of Sets 2.2.Binary Relation 2.3.Representation of Binary Relations on Finite Sets using Graphs and Matrices 2.4.Typical Operations on Relations 2.5.Concept of Multidimensional Relation Lecture 3. Functions. Equivalence Relation 3.1.Function (Functional Relation) 3.2.Types of Functions 3.3.Equivalence Relation Lecture 4. Ordering Relations 4.1.Partial Ordering Relation 4.2.Linear Ordering Relation 4.3.Strong Ordering Relation 4.4.Strong Linear Ordering Relation 4.5.The Largest and Smallest Element in the Set. Supremum and Infimum of a Partially Ordered Set 4.6.Well-Ordering Relation Examples of Typical Exercises for Lecture 4 Lecture 5. Algebraic Systems 5.1.Algebraic Operations 5.2.Definition of the Algebraic System. Algebraic Structure and Relational System 5.3.Groupoid. Semigroup. Group. Subgroup 5.4.Isomorphism of Algebraic Systems Lecture 6. Rings as Algebraic Structures. Boolean Algebra 6.1.Rings as Algebraic Structures 6.2.Application of Ring Theory 6.3.Boolean Algebra Lecture 7. The Eąuinumerous Relation of Sets. Cardinal Numbers 7.1.The Concept of the Eąuinumerous Relation of Sets. Cardinal Numbers 7.2.Countable Sets 7.3.Uncountable Sets 7.4.Cantor-Bernstein Theorem. Comparison of Cardinal Numbers Lecture 8. Introduction to Logic. Classical Propositional Logic as the Basis of Mathematical Logic 8.1.Introduction to Logic 8.2.Classical Propositional Logic. The Statement and its Mathematical Formalization 8.3.Logical Operations on Statements Lecture 9. The Language of Propositional Calculus. Zero-One Method of Checking the Tautology of Expressions 9.1. The Concept of Formal Language. Formalization and Interpretation Procedures 9.2.The Language of Propositional Calculus 9.3.Formulas of Propositional Logic as Functions of Statement Variablesl02 9.4.Types of Propositional Logic Formulas 9.5.Zero-One Method of Checking the Tautology of Formulas 9.6.Logically Equivalent Formulas Lecture 10. Inference Rules in the Classical Propositional Logic. Propositional Logic as a Formal Axiomatic System 10.1.The Concept of Inference. Formalization of Inferences. The Inference Scheme 10.2.Typical Inference Rules 10.3.Theory as the Most Developed Form of Knowledge. Types of Theories 10.4.Formal Axiomatic Systems 10.5.Propositional Logic as a Formal Axiomatic System Lecture 11. Logical Functions. Elements of Algebra of Logic 11.1.The Concepts of a Logical Variable and a Logical Function 11.2.Some Properties of Logical Functions 11.3.Algebras of Logic 11.4.Application of Binary Boolean Algebra Lecture 12. Elements of Logic of Concepts 12.1.Connotation and Denotation of Concept 12.2.Classification of Concepts 12.3.Relations Between Concepts 12.4.Operations on Concepts Lecture 13. Elements of Predicate Logic 13.1.Defmitions and Properties of Predicates 13.2.Types of Predicates. The Truth Set of the Predicate 13.3.Logical Operations on Predicates 13.4.Quantifier Binding Operations on Predicates 13.5.Square of Opposition Lecture 14. Predicate Logic as a Formal Axiomatic System. Presentation of Basic Concepts of Set Theory Based on Predicate Logical Expressions 14.1.Predicate Logic as a Formal Axiomatic System 14.2.Presentation of the Basic Concepts of Set Theory Based on Expressions of Predicate Logic Lecture 15. Introduction to the Theory of Fuzzy Sets and Fuzzy Logic 15.1.About the Fuzzy Approach in Mathematics and Logic 15.2.Fuzzy Sets. Operations on Fuzzy Sets. Fuzzy Sets Algebra 15.3.Distances Between Fuzzy Sets. Fuzzy Relations 15.4.Fuzzy Statements. Logical Operations on Fuzzy Statements 15.5.Fuzzy Variable and Linguistic Variable