Hi everyone,

The answer key for the Final Exam Review Sheet is now complete (it can be found in Classroom Resources / Exam Reviews ).

Regards,

Prof. Reitz

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Hi everyone,

The answer key for the Final Exam Review Sheet is now complete (it can be found in Classroom Resources / Exam Reviews ).

Regards,

Prof. Reitz

- OpenLab #1: Advice from the Past – 2019 Fall – MAT 2071 Proofs and Logic – Reitz on OpenLab #7: Advice for the Future
- Franklin Ajisogun on OpenLab #7: Advice for the Future
- Franklin Ajisogun on OpenLab #3: “Sentences”
- Franklin Ajisogun on OpenLab #6: Proof Journal
- Jessie Coriolan on OpenLab #7: Advice for the Future

- Example of an uncountable subset of $\mathbb R$ which cannot be proved to have the same cardinality as $\mathbb R$ February 22, 2024I am new to mathematical logic so forgive me if this is a bad question. I understand that the Continuum Hypothesis (CH) is independent of ZFC and therefore there exist models of ZFC in which the CH is false. In such models, by the very definition of CH being false, there must exist a set […]Oliver
- Do there exist sets that cannot be constructed? February 22, 2024Do there exist sets which cannot be constructed? Do there exist subsets of the real numbers that cannot be constructed? By constructed, I mean that it is possible to give a description of how to build the set. I'm assuming ZF(C) axioms.Oliver
- Is it possible to perform induction on the integers? February 21, 2024On a recent assignment, I had a question where I had to prove a certain statement to be true for all $n\in\mathbb{Z}$. The format of my proof looked like this: Statement is true when $n=0$ "Assume statement is true for some $k\in\mathbb{Z}$" Statement must be true for $k+1$ Statement must be true for $k-1$ My […]June Richardson
- Is $F(x) \in z$ absolute February 21, 2024For an absolute Function F (meaning that the formula y=F(x) is absolute), is there a proof that $F(x) \in z$ is an absolute Formula? This Lemma from Kunen applied for $\Phi(w,z)$ being $w \in z$ and $G_1=F$ says there should be: [![Lemma from Kunen][1]][1] However the proof of the lemma is not convincing so i […]Rubids
- Why is having T in every row under two propositions is not sufficient to say that they are equivalent? [duplicate] February 21, 2024Task on propositional logic: "Suppose you create a truth table for A and B, both formulas in propositional calculus, and have a look at the columns below the main connectives of A and B. When do we know for sure that A ≡ B is true?" My understanding is that this option should be correct: […]Роман Кирьянов
- What does $\forall x (Triangle(x) \iff \exists y (Square(y) \land AboveOf(x,y)))$ imply? February 21, 2024I'm trying to make a Tarski World for this structure: $$\forall x (Triangle(x) \iff \exists y (Square(y) \land AboveOf(x,y)))$$ I think that it means the following: Element is a triangle if and only if there is a square below it. So every triangle must have squares below it. There is a square that is below […]Роман Кирьянов
- 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
- 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

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