#Math213

Terms

Logic

Logic is the basis of all mathematical reasoning:

  • Syntax of statements
  • The meaning of statements
  • The rules of logical inference

Proposition(命题)

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注意：

  • 命题不能是一个疑问句或者命令；
  • 命题要么真要么假，不能涉及变量,命题一定能判断真假

Compound Propositions: Combinations of several propositions

Logical Connectives

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  • 注意 p->q 的各种表述unless 与 only if
    注意 p->q 准确应理解为 p 蕴含于 q (Not p; p implies q)

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  • 逆命题 (converse)，反命题 (inverse)，逆否命题 (contrapositive)
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  • Biconditional 的表述
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Propositional Application and Equivalence

Application

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Equivalence

Specific Terms

  • Tautology: 恒真
  • Contradiction: 恒假
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Logical Equivalences

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等价 ->Truth Table 上两个命题同真同假即可
等价的证明

  • truth table 上证明同真同假
  • 直接用逻辑算符证明

Boolean Logic
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Proof

  • Logical Expression
  • Truth Table

Limitation of Propositional Logic

引入 Predicates(断言/谓词) 与 quantifier(量词)