Summary of Discrete Mathematics Knowledge Points
Chapter 2 Propositional Logic
1.→, the front key is true, the back key is false to be false; <— >, the same is true, the difference is false;
2. The main disjunctive paradigm: the sum of minimal terms (m); the main conjunctive paradigm: the product of maximal terms (M);
3. When seeking the minimum term, the positive argument of the proposition is 1 and the negative is 0. When seeking the maximum term, the opposite is true;
4. When seeking the maximum and minimum terms, each variable or the negation of the variable can only appear once. When the minimum term is sought, the variable is not enough to be true, and when the maximum term is not enough, the variable is not enough to disjunction false;
5. When seeking the paradigm, in order to ensure a good coding, the propositional variables are best written in the order of P, Q, R;
6. The item with the value of 1 in the truth table is the minimum item, and the item with the value of 0 is the maximum item;
7. There are 2n minimal or maximal terms for the n variables, and the 2n is (0~2n -1), which is just the main disjunction plus the main conjunction after simplification;
8. There is no subjective conjunctive paradigm for the permanent true form, and no subjective disjunctive paradigm for the permanent false form;
9. Method of inferring implication (=>): truth table method; analytical method (assuming that the previous key is true and then the key is true; assuming that the previous key is false and the key is also false afterwards)
10. The inference calculation method of propositional logic: P rule, T rule
① Truth table method; ② Direct proof method; ③ Reduction method; ④ Additional premise method;
Chapter 3 Predicate Logic
1. Unary predicate: the predicate has only one individual, and the unary predicate describes the nature of the proposition; Multiple predicate: the predicate has n individuals, and the multiple predicate describes the relationship between the individuals;
2. The universal quantifier uses implication →, the existence quantifier uses conjunction ^;