**Week 4 Assignments**

**Written work** – none

**WeBWorK **– Assignment #3 and Assignment #4, due Tuesday, September 20th, at midnight.

**OpenLab **– none

**STUDY** – for your first exam, taking place next Thursday, 9/22, during the first hour of class.

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**Week 4 Assignments**

**Written work** – none

**WeBWorK **– Assignment #3 and Assignment #4, due Tuesday, September 20th, at midnight.

**OpenLab **– none

**STUDY** – for your first exam, taking place next Thursday, 9/22, during the first hour of class.

- Within a distribution of primes, $p$, among the integers, are the total areas of circles or rectangles larger? January 25, 2022Suppose you have a distribution of primes, $p_1, p_2, ..., p_n, p_{n+1}, ....$ For each $p$, draw a circle with $radius$ $=$ $p$ and a rectangle with $height$ $=$ $p$ and $length$ $=$ $(p_{n+1}-p_n)$. Which is larger, the total area of the circles or rectangles?C0lt4rty5
- What does close mean in first order logic? January 24, 2022I just ran across this statement in a logic book A predicate can’t be true or false until a specific value is substituted for the variables, and the quantifiers ∀ and ∃ “close” over a predicate to give a statement which can be either true or false. I think I understand the "specific value" part; […]147pm
- Induction to Define Permutation (Propositional Logic)? January 24, 2022For a well-formed formula φ, use induction to define permutation(φ), which is the number of logically equivalent formulas obtained from φ by changing the order of the operands in the logical connectives in φ e.g., permutation(p ∨ q) = 2 because p ∨ q ≡ q ∨ p, permutation(p → q) = 1 because p […]uwu
- Axiomatizability of class of the language $L=\{ = \} $ January 24, 2022I was solving a mock exam and there is a "tricky" question, for me at least. It seem to me impossible that question 1) and 4) are both true. I would love to understand Let $L$ a language with the symbol $ \{=\} $ and $C$ a class of $L$-structure. We say that $C$ is […]3m0o
- Explain why $\varphi$ is a tautology, and $\psi$ is a contradiction (unsatisfiable formula) January 24, 2022Let $\varphi \rightarrow \psi$ be a contradiction with well-formed formulas $\varphi$ and $\psi$. Explain why $\varphi$ is a tautology and $\psi$ is a contradiction (unsatisfiable formula). We have begun propositional logic in class and this is an example for lecture. I am confused how to prove this seeing as it doesn't seem plausible to use […]uwu
- Looking for "desktop reference" for logic January 24, 2022By "desktop reference" I mean a book that aims to be comprehensive and self-contained, rather than didactic1. The best example I can think of of the sort of book I am looking for is Jech's Set Theory. Also, by "self-contained" is mean that it includes all non-trivial proofs. The book should cover, at least, propositional […]kjo
- Uniform bound on the sets defined by a formula January 24, 2022I want to show that if we consider a strongly minimal model $M$, then for every formula $\varphi(x,y)$, there is a integer $n_\varphi$ such that whenever $\varphi(M,a)$ is finite, its cardinal is less than $n_\varphi$. What I tried is to first look at algebraically closed fields, because it is a theory that is quite easy […]Sora
- A sentence valid in all finite structures January 24, 2022Consider a first order language $L$. Let $S$ be an $L$-sentence true in all finite $L$-structures but false in some infinite $L$-structure. The completeness theorem implies $S$ can not be proven by usual means. Yet, is there another way to establish $S$ is true in all finite models? Another question is whether we can write […]Holy Moly
- Is a clopen set a paraconsistent object? January 24, 2022I hope this question makes sense, the doubt just arose out of curiosity. Knowing that there are sets that are open and closed at the same time, I wonder if this has any relation to paraconsistent logic, since we could say that these clopen sets have properties of the type ($p\wedge \neg p$) if we […]Luis Alexandher
- What do semi-formal proofs that use objects from different areas mathematics look like when completely formalized? January 24, 2022What do semi-formal proofs that use objects from different areas mathematics look like when completely formalized? For example: Using graphs and planarity to show that circles cannot be used to draw n-Venn diagrams for n grater than or equal to 4. or Using properties of recursion and combinatorics to prove a lower bound on the […]stam_a

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