1. Set theory: Set theory is the basis of discrete mathematics, which studies sets and their basic concepts such as operations, relations and functions. Set theory provides a theoretical basis for other discrete mathematics branches.
2. Graph theory: Graph theory studies graphs and their properties, including the concepts of vertices, edges, paths and loops. Graph theory is widely used in computer science, communication network, transportation and other fields.
3. Logic and Boolean algebra: Logic studies concepts such as propositions, predicates and reasoning, while Boolean algebra is a special form of logic, which studies Boolean variables and their operations. Logic and Boolean algebra have important applications in computer hardware design, software programming and other fields.
4. Combinatorial mathematics: Combinatorial mathematics studies the combinatorial properties of discrete objects, including concepts such as permutation, combination and binomial coefficient. Combinatorial mathematics is widely used in probability theory, statistics, computer science and other fields.
5. Mathematical logic: Mathematical logic studies the formal representation of propositions and their reasoning rules, including propositional formulas, truth tables, axiomatic systems and other concepts. Mathematical logic has important applications in computer science, artificial intelligence and other fields.
6. Proof theory: Proof theory studies the laws and methods of mathematical proof, including the concepts of proof method, proof structure and proof strategy. Proof theory has important applications in computer science, software engineering and other fields.
7. Discrete probability theory: Discrete probability theory studies discrete random variables and their probability distribution, including concepts such as probability quality function, conditional probability and independence. Discrete probability theory is widely used in computer science, statistics and other fields.
8. Algorithm analysis: Algorithm analysis studies the efficiency and complexity of the algorithm, including the concepts of time complexity, space complexity and algorithm optimization. Algorithm analysis has important applications in computer science, software engineering and other fields.
In a word, the core logic of discrete mathematics involves set theory, graph theory, logic and Boolean algebra, combinatorial mathematics, mathematical logic, proof theory, discrete probability theory and algorithm analysis. These logics are interrelated and isomorphic to the theoretical system of discrete mathematics.