# Tag: visual math

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- Irving M. Copi, Logic 14th, 554pg 11 question about error February 21, 2024premise 1 premise 1: (∀x)(Fx→Gx) premise 2: (∃x)(Fx ∧ ~Gx) conclude: (∃x)(Gx∧~Fx) Fa ∧ ~Ga 2. E.I. Fa->Ga 1. U.I. Fa 3. Simp. ~Ga 3. Simp Ga 4, 5. M.P. ~Fa 4, 6. M.T. Ga ∧ ~Fa 7, 8. Conj. (∃x)(Gx∧~Fx) 9. E. G. Q.E.D. The book suggests that this argument is a valid argument. […]김성도
- Encoding the fist element of an ordered pair February 21, 2024Assuming we are working in axiomatic set theory, such as $ZFC$ or $NBG$ can we, for all ordered pairs $(x, y)$ find a monadic predicate, call it $First$ such that $First((x, y))=x$ Is such a thing possible if we are using Kuratowski's definition of the ordered pair, namely $(x, y) = \{ \{x \}, \{ […]Shthephathord23
- Parsing this wff efficiently February 21, 2024I have the wff: $$\alpha = (((\neg(A_1\rightarrow (A_3\vee (\neg A_2))))\wedge(A_4\wedge(\neg A_1)))\rightarrow((\neg(A_3\vee A_2))\rightarrow(((\neg A_1)\wedge A_4)\vee A_3)))$$ I've already parsed through $12$ of the $16$ possibilities in the truth table. If we let $$\beta = ((\neg(A_1\rightarrow (A_3\vee (\neg A_2))))\wedge(A_4\wedge(\neg A_1)))$$ and $$\gamma = ((\neg(A_3\vee A_2))\rightarrow(((\neg A_1)\wedge A_4)\vee A_3))$$ Then $\alpha = (\beta \rightarrow \gamma)$. I've already shown […]Cotton Headed Ninnymuggins
- How can mathematical logic try to model math, when mathematics are used to define mathematical logic? February 20, 2024I've done so far a few courses in logic and formal verification, and I've always wondered: mathematical logic, at least as Hilbert envisioned, tries to model mathematics. Formally define what a "true" statement is, or why proving something (at least in a sound system) makes it true. But, every logic course uses mathematics in its […]sadcat_1
- Can I combine axioms to have less properties to verify independently? February 20, 2024For example, given that a linear function is defined by its satisfying the properties $f(x+y)=f(x)+f(y)$ and $f(ax)=af(x)$, would it be okay to only check $f(ax+by)=af(x)+bf(y)$, or maybe even $f\left(\frac ab x+y\right)=\frac abf(x)+f(y)$ and put $c=\frac ab$?AnotherSherlock
- NBG the intersection of a set and a class February 20, 2024In this post I will assume the NBG set theory For all classes $X$ let $M(X)$ mean $(\exists T)(X \in T)$ i.e. $X$ is a set and not a proper class. Prove that $\left\{X \subseteq Y, M(Y) \right\} \vdash_{\text{NBG}} M(X)$ My ideea for the proof. We know that for all classes $X$ and $Y$ that […]Shthephathord23
- Give formal proof [closed] February 20, 2024⊤ ⊢ ((A ↔ B) ∨ (B ↔ C)) ∨ (A ↔ C) I have gotten this far... |_ -(((A ↔ B) ∨ (B ↔ C)) ∨ (A ↔ C)) :AS | |_ -((A ↔ B) ∨ (B ↔ C)) :AS | | |_ ((A ↔ B) ∨ (B ↔ C)) :AS | | | […]Mia Solorsano-Sobarzo
- How to encapsulate my argument using symbolic logic February 20, 2024I am working on logic for the first time and I was wondering what the best way to translate the following argument is: Most current senators of the U.S. are men. Ted Cruz is a current U.S. senator. $\therefore$ Ted Cruz is a man. My attempts are below, however someone has suggested that they might […]screamingstudent
- Evaluating whether an argument is valid February 19, 2024I want to determine whether the following argument is valid (please don't give any answers, I just need some feedback on whether I'm on the right track): Melania Trump is Donald Trump’s wife. The president of the United States’s wife is the first lady of the U.S. Melania Trump is the first lady of the […]screamingstudent
- Prove that following argument is valid February 19, 2024Determine whether the following arguments is correct or not. If it rains in Spain, then Steffi will win and Gabriella will lose. If Gabriella loses then Germany will become the team champion. If Steffi wins, then Jennifer will be disappointed. If it doesn't rain in Spain, then Monica will win. Therefore either Jennifer will be […]Old

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