《离散数学》双语教学 第一章 真值表，逻辑和证明
《离散数学》双语教学 第一章 真值表，逻辑和证明
CHAPTER 1
TRUTH TABLES, LOGIC, AND PROOFS
Glossary
statement, proposition:命题 logical connective:命题联结词
compound statement:复合命题 propositional variable:命题变元
negation:否定(式)
truth table:真值表
相邻色conjunction:合取 disjunction:析取 propositional function:命题公式
fallacy: 谬误
syllogism:三段论
universal quantification:全称量词化 existential quantification:存在量词化 hypothesis(premi): 假设～前提～前件 conditional statement, implication:条件式～蕴涵式 conquent, conclusion:结论～后件 conver:逆命题
contrapositive:逆否命题
biconditional, equivalence:双条件式～等价
(逻辑)等价的 logically equivalent:
contingency:可满足式
tautology:永真式(重言式)
contradiction, absurdity:永假(矛盾)式 logically follow:是…的逻辑结论 argument:论证
axioms:公理 日本大学动漫
第 1 页 共 47 页 2010-12-27 含硫氨基酸
《离散数学》双语教学 第一章 真值表，逻辑和证明 postulate:公设
rules of reference:推理规则
modus ponens:肯定律 modus tollens:否定律
reductio ad absurdum:归谬律
proof by contradiction:反证法
counterexample:反例 minterm:极小项
disjunctive normal form:主析取范式
maxterm:极大项
conjunctive normal form:主合取范式
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《离散数学》双语教学 第一章 真值表，逻辑和证明
本章内容及教学要点:
1.1 Statements and Connectives
教学内容:statements(propositions)～compound statement～connectives:negation～conjunction～disjunction～truth tables 1.2 Conditional Statements
教学内容:implications(conditional statements)～biconditional～equivalent～and quantifications
亘古不变是什么意思
1.3 Equivalent Statements
教学内容:logical equivalence～conver～inver～contrapositive～tautology～contradiction(absurdity)～contingency～properties of logical
connectives
1.4 Axiomatic Systems: Arguments and Proofs
教学内容:rules of reference～augument～valid argument～hypothes～premis～law of detachment(modus ponens)～syllogism～modus tollens～addition～proof by contradiction 1.5 Normal Forms
78年今年多大
教学内容:minterm～disjunctive normal form～maxterm～conjunctive normal form
定理证明及例题解答
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贝壳花《离散数学》双语教学 第一章 真值表，逻辑和证明
夜观星空Logic, developed by Aristotle, has been ud through the centuries in the development of many areas of learning including theology, philosophy, and mathematics. It is the foundation on which the whole structure of mathematics is built. Basically it is the science of reasoning, which may allow us to determine statements about mathematics whether are true or fal bad on a t of basic assumptions called axioms. Logic is also ud in computer science to construct computer programs and to show that programs do what th
ey are designed to do.
逻辑学是研究人的思维形式的科学. 而数理逻辑是逻辑学的一个重要分支～
是用数学形式化的方法研究思维规律的一门学科. 由于它使用了一套符号来简洁
地表达出各种推理的逻辑关系～故它又称符号逻辑.
数理逻辑用数学方法研究推理、利用符号体系研究推理过程中前提和结论之
间的关系. 数理逻辑的主要内容:逻辑演算(L和L)、公理化集合论、模型论、S p
构造主义与证明论. 数理逻辑在电子线路、机器证明、自动化系统、编译理论、
算法设计方法方面有广泛的应用.
The rules of logic specify the meaning of mathematical
statements. Logic is the basis of all mathematical reasoning, and it has practical applications to the design of computing machines, to system specifications, to artificial int
elligence(AI), to computer programming, to programming languages, and to other areas of computer science, as well as to many other fields of study.
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《离散数学》双语教学 第一章 真值表，逻辑和证明
1.1 Statements and Connectivess(命题和联结词)
命题逻辑研究的对象是命题及命题之间的逻辑关系.
Propositions are the basic building blocks of logic. Many mathematical statements are constructed by combining one or more propositions.
定义1.1.1 A proposition is a statement or declarative ntence that is either true or fal, but not both,命题是一个非真即假的陈述句,.
脚夫
