**Week 2 Assignments**

**Written work** – none

**WeBWorK **– Assignment #1 and #2, due Tuesday, September 6th, at midnight.

**OpenLab **– OpenLab #2, due Thursday, September 8th, at the start of class.

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### Logic on Math StackExchange

- Trying to proof two XOR instances October 11, 2024I have proof (truth table) that both instances of XOR are correct. Which means both instances have to be equal to each other. Yet, I am missing the insight to get from one to the other. My (math) background is rather modest but I would be pleased if someone could help me apply the laws […]fabio-dc
- Logic which depends on perspective? [closed] October 11, 2024How would you implement with known mathematical tools and theory logic which depends on some point of view or perspective? (mathoverflowUser
- How to logically formalize two-player with imperfect information? October 11, 2024It is known that any first-order formula with no free variables is equivalent to a perfect information game with finitely-many turns, that is, for example, the formula $\forall x, \exists y, x\neq y$ describes the game « Alice plays $x$ first, and then, Bob, knowing that Alice played $x$, plays $y$, and then the referee […]Plop
- Am I right about causality? [closed] October 11, 2024C(cause, effect): "The cause is the cause of the effect." ∃cause∀effect(C(cause, effect)): "There exists a cause that is the cause of all effects." The negation of statement 2 is ∀cause∃effect(¬C(cause, effect)): "Not all causes are the cause of some effect." = "Some effects have no cause." Generally, if there is an effect, it is believed […]Display name
- A question about tautologies in zero order logic [closed] October 10, 2024Assume τ be a well formed formula that has the property that (A → τ ) is a tautology for every sentense symbol A. Prove that τ is a tautology.Rohit Mutyala
- Is the class of all Hamiltonian graphs axiomatizable in second-order logic? October 10, 2024Is the class of all Hamiltonian graphs axiomatizable in second-order logic? Definitions: Hamiltonian graph is a graph s.t. there exists a cycle that goes exactly once through all vertices a class is axiomatizable in second-order logic if there is a set of second-order sentences $T$ s.t. (using standard semantics) $G\models T \iff G\text{ "is Hamiltonian"}$ […]Timotej Šujan
- 1-fragments of the Naive Set Theory with independent self-membership of the main set October 9, 2024I'm doing some research in non-trivial fragments of Naive Set Theory ($\mathsf{NST}$). By fragment of $\mathsf{NST}$ I mean that some instances of unrestricted comprehension (UC) are left out. UC is for me the following schema: $\exists y\forall x(x\in y \leftrightarrow \varphi(x))$ s.t. $y$ is not free in $\varphi$. The base fragment $\forall\mathsf{CL{+}ext}$ is then just […]Timotej Šujan
- Is there an effective procedure to find a Gödel sentence? [duplicate] October 8, 2024Let $\def\N{\mathcal{N}}$ $\N$ be some (powerful enough) theory of arithmetic. Is there an effective procedure to find a Gödel sentence $A$ in $\N$? That is, a sentence for which $$\vdash A \iff \neg P(A).$$ To be clear, this means building a computer program that runs through all sentences in $\N$, expressed as finite strings of […]Sam
- Solving $P \implies Q, \neg R \implies \neg S, \neg Q \lor S $ [closed] October 8, 2024Steps for solving \begin{align} P \implies Q \\ \neg R \implies \neg S \\ \neg Q \ \lor \ S \end{align} The teacher said $\therefore \neg P \ \land \ R $, however I got $\therefore \neg P \ \lor \ R $ If my notation is confusing or wrong, here's the statement in English: […]ConfusedButterfly
- "If there exists $Y {\subsetneq} X$ such that $P$ holds, then there exists $x {\not\in} Y$ such that $Q$ holds" October 8, 2024Let $X$ be a nonempty set. If there exists a subset $Y \subsetneq X$ such that property $P$ holds, then there exists an $x \not \in Y$ such that property $Q$ holds. I'm trying to determine the contrapositive of the above conditional statement. My initial guess: If for every $x \not\in Y$, $\neg Q$ holds, […]A.Z

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