**Written work, **Due Tuesday, October 30, in class. GCD Problems:

Chapter 4 p.101: 27, 28

Chapter 5 p.110: 29, 31

**WeBWorK **– none

**OpenLab **– OpenLab #6: Proof Journal due Tuesday, November 6th, in class (two weeks)

Skip to the content

**Written work, **Due Tuesday, October 30, in class. GCD Problems:

Chapter 4 p.101: 27, 28

Chapter 5 p.110: 29, 31

**WeBWorK **– none

**OpenLab **– OpenLab #6: Proof Journal due Tuesday, November 6th, in class (two weeks)

- 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

- The Proof of the Model Existence Lemma and Gödel's Incompleteness Theorem [duplicate] November 5, 2024Model Existence Lemma: given a consistent set of sentences $S$ in the language $L$, there is a model of $S$. I'm sure this is just a silly confusion. The usual proof of the Model Existence Lemma requires us to construct a complete, consistent, witnessing extension of $S$. If $S$ was to contain Peano Arithmetic $(\textbf{PA})$, […]Sam
- Confused about a possible asymmetry between $\land$ and $\lor$ in proof theory November 5, 2024Currently, I believe two things (please correct me if I'm wrong): $\def\f{\phi} \def\y{\psi} \def\LLL{\mathcal{L}} \def\S{\Sigma}$ given sentences $\f,\y$ in the language $\LLL$, and a theory $\S$, we have that $\S \vdash \f\land \y$ if and only if $\S\vdash \f$ and $\S\vdash \y$. Proof: for the $(\Rightarrow)$ direction, simply use the deduction rule $$\frac{\f\land\y}{\f}$$ or any […]Sam
- The difference between biconditional and equivalence [duplicate] November 5, 2024My question is simple is the Tautology $p\Leftrightarrow q$ and $a \equiv b $ the same ?bigbng
- Symbolising "Every team in league S has exactly one rival in league S" November 5, 2024Given Predicates: T(x, y): Team x plays in league y. R(x, y): Team x is a rival of team y. Note: R is symmetric: R(x, y) = R(y, x). Statement to Translate: Every team in league S has exactly one rival, that is also in league S. My Solution Attempt: $$\forall x \left( T(x, S) […]utterdisaster
- Why must $S$ be extended to a complete set of sentences to prove the Model Existence Theorem November 5, 2024Model Existence Theorem: let $S$ be a consistent set of sentences in the language $L$. Then $S$ has a model. The proof usually extends $S$ to a completely consistent set $T$ of sentences with witnesses. I understand why the extension $T$ needs to have witnesses: in order for statements of the form $\exists x\phi(x)$ to […]Sam
- Context explanation and what is the MLA equivalent? For.. [closed] November 5, 2024What is a context explanation for referencing &/or/@ citatiom Creation? Including tm/™©® academic/pro/biz/media that is a MLA equiv for all and where could ℹ️ and this or a source for different contexts, history, legal, examples, organizations that police such usage, lawsuits that include any and online or offline no matter location? any answers are welcomed […]j. M.
- "Spectrum" of a Heyting category November 5, 2024Fix a Heyting algebra $H$. By Stone duality for distributive lattices, we know that we can embed $H$ into the lattice of open sets of the space $\mathrm{Spec}(H)$ given by the set of all prime filters on $H$. Then, we also know that the co-Heyting algebra $H^{op}$ embeds into the lattice of closed sets of […]safsom
- Translating syllogisms [duplicate] November 5, 2024Are there tables of set-theoretic equivalences to syllogistic formulas? Or is there a standard way of translating a syllogism into the languages of first-order logic and set theory?inkd
- Can the standard model $M$ of arithmetic be described as that for which any $m\in M$ is of the form $s(\dots s(0)\cdots )^M$? November 5, 2024Can the standard model $M$ of arithmetic be defined (up to isomorphism) as that for which any element $m$ of $M$ is the semantic meaning of $$s(\cdots s(0)\cdots )$$ for a finite number of applications of $s$?Sam
- Logic exercise: prove that $a = b, \phi(a) \models \phi(b)$ November 4, 2024I just wish to know if I'm correctly proving the the following semantic consequence: $\def\f{\phi} \def\MMM{\mathcal{M}}$ $$a = b, \f(a) \models \f(b),$$ for arbitrary constants $a,b$, and for an arbitrary formula $\f(x)$ with a unique free variable $x$. Specifically, I wish to know if I can appeal to the meanings $a^\MMM,b^\MMM,\f^\MMM$ for $a$, $b$, and […]Sam

"Math Improve"
.999
1
assignment
assignments
calculus
calendar
Doodling
exam #3
exam 3 grades
final papers
grading criteria
grading policy
graph theory
group paper
group project
homework
logic
mathography
metacognition
only if
openlab
OpenLab #4: Bridges and Walking Tours
OpenLab7
OpenLab 8
OpenLab8
Open Lab 8
openlab assignment
perfect circle
points
presentation
project
resource
rubric
semester project
spring classes
vi hart
ViHart
visual math
Wau
webwork
week 8
week 14
welcome
written work

© 2024 2018 Fall – MAT 2071 Proofs and Logic – Reitz

Theme by Anders Noren — Up ↑

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

top

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

## Leave a Reply