Chapter 65438 +0 Propositional Logic

Basis: definition and explanation of conjunctions and propositional formulas; Equivalence, implication and duality; ? Type of formula; ? Common minimal connection phrases; ? Major events and minor events and their properties; ? Solution of two main paradigms

Chapter II Predicate Logic

Basis: predicate and propositional function, quantifier;

Constraint variables and free variables's authority and judgment; Type of formula; ? Predicate equivalence and implication; ? Solution of toe-in normal form;

Translation of propositions, first-order logical reasoning, various reasoning rules and their applications, reasoning formats.

Chapter III Collection

Operation of set (intersection and complement, symmetry difference); ? Principle formula of inclusion and exclusion; Cartesian products and ordered pairs

Chapter IV Relations

Three special relationships (identity relationship, generality relationship and emptiness relationship); ? Relational operations (inverse, synthesis);

Transformation and solution of three representations of relationship (set, graph and matrix); ? The judgment and proof of the five properties of the relationship, as well as the reflection in various representations;

Mutual solution and proof of compatibility relation and covering, equivalence relation and division (equivalence class); ? Definition and properties of partial order relation, related concepts (max-min element, max-min element, upper and lower bounds, minimum upper bound, maximum lower bound; Existence and uniqueness) and its judgment

Chapter V Functions

Discrimination of Three Special Functions and Synthesis of Functions

Chapter 6 General Properties of Algebraic Systems

Proof and solution: the definition of algebraic system, the operation on set (computable, unique result, closed); 6 algorithms, 3 special elements (existence and uniqueness) and their reflection in the operation table (pay attention to the requirements of left and right directions when proving some properties); ? Subalgebra, operation of product algebra, special elements; ? Common examples of the above concepts

Chapter VII Typical Algebraic Systems

The connection and difference, discrimination and proof of semigroup, unitary semigroup (unique point) and group, and the solution of special elements;

The nature of group, the concept and judgment of subgroup; ? The order of groups, the order of elements, and the generation of subgroups;

Definition and properties of lattice (two kinds), duality of lattice, definition and properties of distributive lattice, bounded lattice, complement (existence and uniqueness), determination of complement, definition and properties of Boolean algebra;

Common examples of the above concepts