MY-ASSIGNMENTEXPERT™可以为您提供 math MATH5051 Mathematical Logic数理逻辑的代写代考和辅导服务！
这是俄亥俄州立大学 数理逻辑的代写成功案例。
MATH5051课程简介
Syntax and semantics of sentential logic, syntax and semantics of first-order logic, compactness of first-order logic, Goedel's completeness theorem, theories and models of theories, Goedel's incompleteness theorems; computability.
Prereq: 4547 (547), 4580 (580), Grad standing, or permission of department. Not open to students with credit for 648 or 649.
Prerequisites
Mathematical logic emerged in the mid-19th century as a subfield of mathematics, reflecting the confluence of two traditions: formal philosophical logic and mathematics.[3] “Mathematical logic, also called ‘logistic’, ‘symbolic logic’, the ‘algebra of logic’, and, more recently, simply ‘formal logic’, is the set of logical theories elaborated in the course of the last Nineteenth Century with the aid of an artificial notation and a rigorously deductive method.
MATH5051 Mathematical Logic HELP（EXAM HELP， ONLINE TUTOR）
Let’s consider a propositional language where
p means “Paola is happy”,
q means “Paola paints a picture”,
$r$ means “Renzo is happy”.
Formalize the following sentences:
- “if Paola is happy and paints a picture then Renzo isn’t happy”
- “if Paola is happy, then she paints a picture”
- “Paola is happy only if she paints a picture”
Solution.
- $p \wedge q \rightarrow \neg r$
- $p \rightarrow q$
- $\neg(p \wedge \neg q)$..which is equivalent to $p \rightarrow q$
The precision of formal languages avoid the ambiguities of natural languages.
Let $A=$ “Aldo is Italian” and $B=$ “Bob is English”.
Formalize the following sentences:
- “Aldo isn’t Italian”
- “Aldo is Italian while Bob is English”
- “If Aldo is Italian then Bob is not English”
- “Aldo is Italian or if Aldo isn’t Italian then Bob is English”
- “Either Aldo is Italian and Bob is English, or neither Aldo is Italian nor Bob is English”
Solution.
- $\neg A$
- $A \wedge B$
- $A \rightarrow \neg B$
- $A \vee(\neg A \rightarrow B) \quad$ logically equivalent to $A \vee B$
- $(A \wedge B) \vee(\neg A \wedge \neg B) \quad$ logically equivalent to $A \leftrightarrow B$
Let’s consider a propositional langiage where
- $A=$ “Angelo comes to the party”,
- $B=$ “Bruno comes to the party”,
- $C=$ “Carlo comes to the party”,
- $D=$ “Davide comes to the party”.
Formalize the following sentences:
- “If Davide comes to the party then Bruno and Carlo come too”
- “Carlo comes to the party only if Angelo and Bruno do not come”
- “Davide comes to the party if and only if Carlo comes and Angelo doesn’t come”
- “If Davide comes to the party, then, if Carlo doesn’t come then Angelo comes”
- “Carlo comes to the party provided that Davide doesn’t come, but, if Davide comes, then Bruno doesn’t come”
- “A necessary condition for Angelo coming to the party, is that, if Bruno and Carlo aren’t coming, Davide comes”
- “Angelo, Bruno and Carlo come to the party if and only if Davide doesn’t come, but, if neither Angelo nor Bruno come, then Davide comes only if Carlo comes”
Solution.
- $D \rightarrow B \wedge C$
- $C \rightarrow \neg A \wedge \neg B$
- $D \leftrightarrow(C \wedge \neg A)$
- $D \rightarrow(\neg C \rightarrow A)$
- $(\neg D \rightarrow C) \wedge(D \rightarrow \neg B)$
- $A \rightarrow(\neg B \wedge \neg C \rightarrow D)$
- $(A \wedge B \wedge C \leftrightarrow \neg D) \wedge(\neg A \wedge \neg B \rightarrow(D \leftrightarrow C))$
MY-ASSIGNMENTEXPERT™可以为您提供 math MATH5051 Mathematical Logic数理逻辑的代写代考和辅导服务！
