Mathematical Ideas Sam Houston State （数学思想,萨姆。休斯顿的状态）.ppt

Chapter 3: Introduction to Logic Truth Tables and Equivalent Statements Conjunctions Disjunctions Negations Mathematical Statements Truth Tables Alternative Method for Constructing Truth Tables Equivalent Statements and De Morgan’s Laws Conjunctions Conjunction Truth Table Example: Finding the Truth Value of a Conjunction Disjunctions Disjunctions Example: Finding the Truth Value of a Disjunction Negation Example: Mathematical Statements Truth Tables Example: Constructing a Truth Table Number of Rows in a Truth Table Alternative Method for Constructing Truth Tables Equivalent Statements Example: Equivalent Statements De Morgan’s Laws Example: Applying De Morgan’s Laws *? 2008 Pearson Addison-Wesley. All rights reserved *? 2008 Pearson Addison-Wesley. All rights reserved *? 2008 Pearson Addison-Wesley. All rights reserved Chapter 3 Introduction to Logic *? 2008 Pearson Addison-Wesley. All rights reserved 3.1 Statements and Quantifiers 3.2 Truth Tables and Equivalent Statements 3.3 The Conditional and Circuits 3.4 More on the Conditional 3.5 Analyzing Arguments with Euler Diagrams 3.6 Analyzing Arguments with Truth Tables Chapter 1 Section 3-2 Truth Tables and Equivalent Statements The truth values of component statements are used to find the truth values of compound statements. The truth values of the conjunction p and q, symbolized are given in the truth table on the next slide. The connective and implies “both.” F F F F F T F T F T T T p q p and q Let p represent the statement 4 1, q represent the statement 12 9 find the truth of Solution False, since q is false. The truth values of the disjunction p or q, symbolized are given in the truth table on the next slide. The connective or implies “either.” F F F T F T T T F T T T p q p or q Let p represent the statement 4 1, q represent the statement 12 9 find the truth of Solution True, since p is true. The truth