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离散数学逻辑和证明部分的相关概念(英文),是离散数学及其应用第七版与北京交通大学的离散数学课程的个人笔记,章节顺序以书为准,本章内容完全从数学定义上学习,建议看之前读一下王路的逻辑基础做铺垫,深入可以看数理逻辑。
梳理了《国际经济学》教材中国际金融部分的相关考点。具体章节有:外汇和汇率、国际收支及其调整、国际货币体系、国际金融市场与金融组织、金融危机
基础生命科学之组织工程相关知识点总结,组织工程,是一门以细胞生物学和材料科学相结合,进行体外或体内构建组织或器官的新兴学科。
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Logic and Proofs
Propositional Logic
propositions
a declarative sentence that is either true or false
compound propositons
negation
conjunction
disjunction
inclusive or
exclusive or
implication
attention : "p only if q" is equal to "p->q"
converse(逆)
contrapositive(逆否)
inverse(反)
biconditional
Propositional equivalances
tautologies(永真)\contradictions(矛盾)\contigencies(可能)
logically equivalent
use truth tabel
use De Morgan's Laws
constructing new logical equivalences
show two expressions are logically equivalent by developing a series of logically equivalent statements
disjunction normal form(析取范式)
each disjunct consists of a conjunction of atomic formulas or the negation of an atomic formula
conjunction normal form(合取范式)
propositional satisfiability
Predicates and quantifiers
predicate logic
variable
predicates
quantifiers
universal quantifier
existential quantifier
uniqueness quantifier
equivalences in predicate logic
quantifiers as conjunctions and disjunctions
De Morgan's Law for quantifiers
Nested Quantifiers
one quantifier is within the scope of another
order of quantifiers
Rules of Proofs
Modus Ponens(假言推理)
Modus Tollens(取拒式)
Hypothetical Syllogism(假言三段)
Disjunctive Syllogism(析取三段)
Addition(附加)
Simplification(化简)
Conjunction(合取)
Resolution(消解)
Universal Instantiation(UI)
Universal Generalization(UG)
Existential Instantiation(EI)
Existential Generalization(EG)