"命题演算中的等值关系与证明方法"

Ch2.pdf；Ch2;Discrete Mathematics©2002 Liu Aimin (刘爱民)2-1 Propositional Logic Equivalence Calculation2 Learning ObjectivesThis chapter mainly involves one of the two important contents in propositional calculus: equivalence calculation. First, understand the meaning of equivalence of propositional formulas, master the construction of truth tables and two methods of proving equivalence, and proficiently apply them to the simplification and canonical representation of propositional formulas.Basic Content of Propositional Formula Equivalence and Its ProofFunctionally complete set of logical connectivesCanonical representation of propositional formulasDiscrete Mathematics©2002 Liu Aimin (刘爱民)2-2 Basic Concepts of Equivalence RelationshipTwo definitions of equivalence:If two logical forms have the same value for any assignment of truth values to their propositional variables, they are considered equal.A, B equivalence refers to the biconditional A↔B being a tautology, denoted as A⇔B. Equivalence of two propositional forms can be directly proven by constructing truth tables. Equivalence calculation allows for the deduction of many other equivalence formulas based on known equivalence formulas. This deduction process is called equivalence calculation. These known equivalence formulas are usually commonly used equivalence formulas that have been proven, many of which are the main components of Boolean algebra or logic algebra, referred to as equivalence relationship patterns:(1) Double negation law: A ⇔ ¬¬A(2) Idempotent law: (2a) A ⇔ A∧A (2b) A ⇔ A∨A(3) Commutative law: (3a; "... Please note that this text has been generated with the help of AI using the information provided. Therefore, it may not be entirely accurate or reflect the actual content of the original file.