# Tag: Doodling

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- How is 2-SAT in time complexity P? October 7, 2022I know that 3-SAT is NP-complete and that 2-SAT is in P. What is the algorithm for solving 2-SAT in polynomial time?635318657
- Understanding Bounded Quantification October 7, 2022Please help with my understanding of the universal quantifier and its bounded version; You're feedback would be of utmost value. I'm at discrete math stage, so my context is the day to day math. Please note that I'm not mentioning any "universal set" here which gives contradictions, but just "a domain of discourse" at hand, […]medium_o
- How do we augment a NNF to satisfy smoothness October 6, 2022In one of the exercise in the book Modeling and Reasoning with Bayesian Networks, by Adnan Darwiche. He stated that an NNF circuit that satisfies decomposability and determinism can be augmented with additional nodes so it also satisfies smoothness. Does anyone have any insights on how this can be done ?some1fromhell
- How to decide p and q in implication or conditional logic? October 6, 2022Let us take an example of compound proposition- If it is sunny, then we will go swimming. Let p: it is sunny Let q: go swimming This proposition is written as: p$\implies$q But it does not make much sense for the false case i.e., when p is true, and q is false (sunny, no swimming). […]avm
- Constructive Zermelo-Fraenkel set theory is contained in Zermelo-Fraenkel set theory October 6, 2022I'm searching for a book or an article that proves that if a statement can be proved in Constructive Zermelo-Fraenkel set theory then the statement can be proved in Zermelo-Fraenkel set theory (for example, I'm searching for a proof of the fact that every axiom of Constructive Zermelo-Fraenkel set theory can be proved in Zermelo-Fraenkel […]effezeta
- Proving sentence using resolution October 6, 2022I want to prove the following tautology using resolution: $$\exists x \forall y P(y,x) \to \forall x \exists y P(x,y)$$ The negation of the sentence in Skolem normal form is $$\forall y \forall v(P(y,c) \land \neg P(f(y),v))$$ for some function symbol $f$ and constant symbol $c$ and variables $x,y,u,v$ but this seems not unifiable since […]Rudinberry
- How do I prove FORMALLY that $\forall xPx\land\forall xQx\iff\forall x(Px\land Qx)$? October 5, 2022I already understand the statement intuitively, so don't try to give me an intuitive explanation as that will not be helpful. I would certainly be willing to "give my own attempts at solving the problem", but I legitimately have no idea on how to go about it. These "rules" (they're called "rules of inference" I […]Dark Rebellion
- Asking whether $\infty$ is an integer October 5, 2022Consider the extended reals, $\mathbb{R} \cup \{\infty\}$. Suppose we ask the question of whether $\infty$ is an integer. It isn't an integer - that is, it is some non-integral value. But then, by the Archimedean property, there exists an integer larger than it, which is contradictory. It is an integer. But again, by the Archimedean […]Aryan Dugar
- How are axiom schemata of ZF defined (without using sets)? [duplicate] October 5, 2022ZF is defined using axiom schemata, rather than a finite set of axioms. So ZF has an infinite (countable) set of axioms. I realized that in my study of math I probably missed how matching a statement to be an instance of an axiom schema is defined. We can't refer to the fact that schemata […]porton
- Does every non-contradictory formal system have a model in ZF? October 5, 2022Is the following statement true? Every non-contradictory formal system has a model in ZF. This seems true, because non-contradictness and existence of model seems equivalent. But how to prove this?porton

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