离散数学课件_第1章_3[修改].ppt

*;CHAPTER 1 The Foundations: Logic, Sets, and Functions; 学习内容;谓词与量词;问题的提出;问题的解决;含变量的语句;含变量的语句; 〖Example 〗 (1) x is greater than y. P(x, y) (2) x is between y and z. B(x, y, z) ; Note: Propositional function has not a definite truth value. 命题函数没有明确的真值 Once a value has been assigned to the variable x, P(x) becomes a proposition and has a truth value. 当变量x被赋予一个值时，P(x) 变为一个有真假值的命题 The truth value of P(x) can be determined when x is assigned a value. (The variable x is bound.) 当x被指派一个值时，P(x)的真值就能确定了;〖Example 〗 Let P(x) denote the statement x 0. What are the truth values of P(-3), P(0) and P(3)? ;谓词与量词;客体、谓词与量词;客体与客体变元;客体与客体变元;客体、谓词与量词;谓 词;谓 词;命题函数;命题函数;定义：在命题函数中命题变元的取值范围， 称之为论域，也称之为个体域。 例如： S(x):x是大学生，论域是:人类。 G(x,y)：xy， 论域是:实数。 定义：由所有客体构成的论域，称之为全总个体域。它是个“最大”的论域。 约定: 对于一个命题函数，如果没有给定论域，则假定该论域是全总个体域。;客体、谓词与量词; There are two ways to create a proposition from a propositional function: 可以通过两种方式从命题函数中产生命题 1. assigning a value to every variable 对每个变量赋予值 2. quantifying it 对它进行定量 （由量词产生命题）;量 词;量词的种类;存在量词;存在量词; 〖Example 〗Express the following statement as a existential quantification. Some real numbers are rational numbers. （一些实数是有理数）;全称量词;Solution:;〖Example 〗Express the following statement as a universal quantification. All lions are fierce. ;两种量词的区别与联系;Negations of Quantifiers量词的否定;量词的否定;量词的指导变元;例 题;谓词与量词;谓词公式;原子谓词公式;谓词演算公式;谓词演算公式;谓词公式;量词的辖域;量词的辖域;谓词公式;约束变元与自由变元;Binding Variables ;Binding Variables ;约束变元与自由变元;约束变元与自由变元;约束变元与自由变元;谓???公式;约束变元的改名;约束变元的改名;谓词与量词;Translating from English into Logical Expression;〖Example 〗C(x): x is a CS student, E(x): x is an CM student S(x): x is a smart student, U = {all students in our class};No CS student is an CM student. If x is a CS student, then that student is not an CM student. ?x (C(x) ? ? E(x)) There does not exist a CS student who is also an CM student. ? ?x [C(x) ? E(x)