Slide Logic học C4 - Logic Học UEL

Introduction to LOGIC Chapter 4. Propositional Logic (Logic mệnh đề) (Reference: Chapter 6) Faculty of Economic Mathematics, University of Economics and Law Outline Symbols and Translation Truth Functions Truth Tables for Propositions Indirect Truth Tables Argument Forms and Fallacies Simple and Compound Statements (Khẳng định đơn và Khẳng định kép) ▶ A simple statement (Khẳng định đơn)1 is one that does not contain any other statement as a component. ▶ For example, “John is tall” is a simple statement. ▶ A compound statement (Khẳng định phức) is one that contains at least one simple statement as a component. ▶ For example, “It is not the case that John is tall” is a compound statement. ▶ We usually denote a simple statement by an uppercase letter. ▶ In order to express a compound statement by symbols, we use logical operators: negation (phủ định), conjunction (hội), disjunction (tuyển), implication (kéo theo), and equivalence (tương đương). 1 sử dụng cách dịch này để tránh với thuật ngữ categorical proposition Logical Operators (các phép toán logic) Operator Name Logical function Used to translate ∼ tilde negation (phủ định) not, it is not the case that • dot conjunction (hội) and, also, moreover ∨ wedge disjunction (tuyển) or, unless ⊃ horseshoe implication (kéo theo) if ... then ..., only if ≡ triple bar equivalence (tương đương) if and only if Remark: Some textbooks use the ampersand, &, in place of the dot; the arrow, →, in place of the horseshoe; and the double arrow, ↔, in place of the triple bar. Negation ▶ Negation (phép phủ định) is a logical operator that reverses the truth value. ▶ The negation (mệnh đề phủ định) of P is denoted as ∼ P. ▶ The truth table of negation is P True False ∼P False True ▶ Example: ▶ Let P: “The number 7 is prime.” (True) ▶ Then ∼ P: “The number 7 is not prime.” (False) Conjunction ▶ Conjunction (mệnh đề hội) is true only if both propositions are true. ▶ Denoted as P • Q. The components P and Q are called conjuncts (các hạng tử hội) ▶ Truth table: P Q P•Q True True True True False False False True False False False False ▶ Example: P: “7 is prime” (True), Q: “7 is odd” (True). P • Q: “7 is prime and 7 is odd” ⇒ True. Disjunction ▶ Disjunction (mệnh đề tuyển) is true if at least one proposition is true. ▶ Denoted as P ∨ Q. The components P and E are called disjuncts (các hạng tử tuyển). ▶ Truth table: P Q P∨Q True True True True False True False True True False False False ▶ Example: P: “10 is prime” (False), Q: “10 is even” (True). P ∨ Q: “10 is prime or 10 is even” ⇒ True. Implication ▶ Implication (mệnh đề kéo theo) is false only if P is true and Q is false. ▶ Denoted as P ⊃ Q. Its components are called the antecedent (tiền tố) (P) and consequent (hậu tố) (Q). ▶ Truth table: P Q P⊃Q True True True True False False False True True False False True ▶ Example: P: “If a number is divisible by 4” (True for 8), Q: “It is divisible by 2” (True). P ⊃ Q is True.