Hi everyone,

The grades for Exam #3 are posted on the “Grades” page – the exams will be returned on Tuesday. Let me know if you have any questions.

Regards,

Prof. Reitz

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Hi everyone,

The grades for Exam #3 are posted on the “Grades” page – the exams will be returned on Tuesday. Let me know if you have any questions.

Regards,

Prof. Reitz

- Question about Hilbert's axiom for the postive fragment of classical logic September 25, 2023In his axiomization of the positive fragment of Classical Logic, Hilbert included the axiom (B -> A) -> [(C -> A) -> (((B -> C) -> A) -> A)] along with the usual conjunction and disjunction axioms, Weakening and Self Distribution. All of those are good. But this monster is about the most opaque axiom […]Michael Lee Finney
- Axioms as PARTIAL information givers of primitive terms - Enderton's Elements of Set theory September 24, 2023This is an excerpt from Elements of Set theory by Enderton.(p. 11) Our axiom system begins with two primitive notions, the concepts of "set" and "member." In terms of these concepts, we will define others, but the primitive notions remain undefined. Instead, we adopt a list of axioms concerning primitive notions. (The axioms can be […]Harshit Rajput
- How to show that $p∨q, q∨r, p\to ¬r ⊢ q$? September 24, 2023How to prove $p∨q, q∨r, p\to ¬r ⊢ q$ using natural deduction? I don't really know how to go about it since I have 2 or statements, but here is my try. $p∨q$ premise $q∨r$ premise $p\to ¬r$ premise $p$ Assumption 1 $¬r$ $\to e 3,4$ $q$ Assumption 2 I am kinda lost and don't […]User
- How to determine all real numbers such that$ \forall n\in \mathbb{N},\:x^{n+2}\:\le \:x^{n+1}+x^n$ [closed] September 24, 2023I've just started higher education in France in what is called "preparatory classes for engineering schools", and the first chapter that we studied is about logic in discrete mathematics. This is the first time I'm studying discrete mathematics and I find it very abstract, too abstact even (keep in mind I'm only 18 and I've […]Sherif Robov
- Understanding indexed families of sets September 24, 2023So I am looking at this family of sets. It has an indexed set of $[0,1]$ where every $x∈[0,1]= \{y∈R |x_0≠0\ \text{AND} \ x_0≤y≤1 \}$ The question is asking which of the following six statements are true. But I am not interested in the answer, I just want to understand what exactly the indexed set […]Adam R. Johnson
- Understanding logic formulae involving $P(n)$ September 24, 2023I am given that that $n,m,$ and $k$ are positive natural numbers, and have to find out which of the six statements above are true. I know that $P(1)$ is not true, because $1$ cannot be written as $5k,$ where $k$ is a natural number; so, I can rule out the first possibility. But I […]Adam R. Johnson
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- Universal generalization and the Deduction theorem September 24, 2023Universal generalization The rule of universal generalization in FOL is stated as follows: (Gen) From $p$ we may infer $(\forall x)p$ provided $x$ does not occur free in any premiss which has been used in the proof of $p$. I don't understand what this means, particularly for deduction sequences. Given a set of formulae $S$ […]Hernán Ibarra Mejia
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