MATHEMATICAL LOGIC : LECTURE 2 скачать в хорошем качестве

MATHEMATICAL LOGIC : LECTURE 2

✨ Chapter: Mathematical Logic 📌 Overview Mathematical Logic is the foundation of reasoning in mathematics and computer science. It deals with the principles and methods used to distinguish valid arguments from invalid ones. This chapter introduces the language of logic, symbols, and techniques to analyze statements systematically. 🧩 Key Concepts Statements (Propositions): Sentences that are either true or false, but not both. Example: "2 + 2 = 4" (True), "The moon is made of cheese" (False). Logical Connectives: Tools to combine or modify statements. AND (∧) – Both must be true. OR (∨) – At least one must be true. NOT (¬) – Negates the truth value. IMPLIES (→) – If one is true, then the other must follow. IF AND ONLY IF (↔) – Both statements are equivalent. Truth Tables: A systematic way to show the truth values of compound statements under all possible conditions. Tautology & Contradiction: Tautology: Always true (e.g., p\vee
eg p). Contradiction: Always false (e.g., p\wedge
eg p).