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Proofs and Logic

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All posts by Samuel

Samuel open lab 8

November 6, 2015OpenLab AssignmentsOpen Lab 8, wongSamuel

 


She was talking about Pythagorean Theorem with piece of paper.

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RSS Logic on Math StackExchange

  • Calculate necessary deceleration to reach desired differential speed at rear end collisions June 27, 2022
    sorry for disturbing your time. But I just dont know how to solve this problem.. Its about rear end collisions. Let's assume the ego vehicle is driving with 70 km/h and the car behind us aswell. Now we have to decelerate because there is an imminent collision infront. The thing is that the deceleration must […]
    Matahari
  • Alternate proof that infinite complete binary branching tree as a Kripke frame generates the S4-tautologies. June 26, 2022
    The $\mathsf{S4}$ tautologies are precisely the formulas of modal logic that hold in all transitive, reflexive Kripke frames. I think I've found an example of a single Kripke frame, the infinite binary tree with the subpath accessibility relation given below, that's universal in the sense that all tautologies that hold for it (when we vary […]
    Greg Nisbet
  • Names for parts of relational models of modal logic June 26, 2022
    One thing that confuses me about modal logic is the exact meaning of the names Kripke frame, Kripke model, (un)pointed [[thing]], etc. I'd like to know the standard names of different subtuples of $(P, W, R, V, w)$, defined below, so I can have a better understanding of textbooks and articles that talk about modal […]
    Greg Nisbet
  • What is the proof that equational logic is undecidable? June 26, 2022
    Following section 8 of Equational Logic by George McNulty, I understand the approach of reducing this decision to the halting problem by modelling Turing machines with equational theories. The construction is as follows: Let $M$ be a Turing machine with instructions of the form $(a,b,q,r,D)$, where $a$ is the letter read by $M$, $b$ is […]
    Owen
  • What is the image of skolemization? June 26, 2022
    For simplicity, consider first order logic with one binary relation in the signature. Any $\forall x \exists y. \phi(x,y)$ gives rise to skolemization, converting the formula into $\forall x. \phi(x,f(x))$, and by that adding a function symbol to the signature. My question is, what precisely are the cases in which we can go the other […]
    Troy McClure
  • Prove. If $r$ and $s$ are bisquare, then $rs$ is bisquare June 26, 2022
    I am currently learning direct proofs. I couldn't solve the following exercise. Define an integer $m$ to be bisquare iff, $\exists a \in Z, \exists b \in Z, m = a^2 + b^2$. Let $r$ and $s$ be fixed integers. Prove: If $r$ and $s$ are bisquare, then $rs$ is bisquare. My work: Proof. Assume […]
    David
  • Rigorous books on basic computability theory June 25, 2022
    Are there books on basic computability theory in which the authors formally prove computabiltiy of functions? By 'formal proof' I mean writing down explicitly the corresponding turing-machine, or lambda-term or proof that the given function is partial recursive. I would like to avoid as much as possible Church-Turing thesis in my proofs. Which of these […]
    user1071197
  • What is wrong with unsound theories? Can they be of any "practical" use? June 25, 2022
    For purposes of this post, let us restrict our attention to theories of arithmetic even though the question indeed makes sense for other theories. In what follows, assume that $PA$ is consistent. A theory of arithmetic is said to be (arithmetically) sound if every statement it proves is true in the intended model $(\mathbb{N},+,\times,S,0)$. Clearly […]
    Burak
  • If $ p \rightarrow q $ and $q \rightarrow p$ are not tautolgies, is $ (p \rightarrow q) \rightarrow (q \rightarrow p)$ a tautology June 25, 2022
    If found a multiple choice question online: If $(p \rightarrow q) $ is not a tautology and $ (q \rightarrow p) $ is not a tautology, then: $ p \lor q $ is not a tautology $ p \lor q $ is a tautology $ p \land q $ is a contradiction $ (p \rightarrow […]
    talopl
  • If $S5 \vdash \alpha$ then $S4 \vdash \diamond \alpha$ June 25, 2022
    I would like to prove that if S5 proves $\alpha$ then S4 proves $\diamond \alpha$. Here S4 is K plus axioms for reflexivity ($\square \alpha \to \alpha$) and transitivity ($\square \alpha \to \square \square \alpha$), and S5 is S4 plus the axiom $\diamond \alpha \to \square \diamond \alpha$. My attempts: I tried to prove it […]
    Mathplendid

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The OpenLab at City Tech:A place to learn, work, and share

The OpenLab is an open-source, digital platform designed to support teaching and learning at City Tech (New York City College of Technology), and to promote student and faculty engagement in the intellectual and social life of the college community.

New York City College of Technology City University of New York

New York City College of Technology | City University of New York

Support

Help | Contact Us | Privacy Policy | Terms of Use | Credits

Accessibility

Our goal is to make the OpenLab accessible for all users.

Learn more about accessibility on the OpenLab

Copyright

Creative Commons

  • - Attribution
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© New York City College of Technology | City University of New York

Proofs and Logic