**Week 3 Assignments**

**Written work** – None

**WeBWorK **– Start on WeBWorK 3, (it will not be due until Tuesday, 9/25 at midnight).

**OpenLab **– OpenLab #3, due Tuesday, 9/20 (at start of class).

*NOTE: Next week Tuesday 9/18 there are no classes.*

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**Week 3 Assignments**

**Written work** – None

**WeBWorK **– Start on WeBWorK 3, (it will not be due until Tuesday, 9/25 at midnight).

**OpenLab **– OpenLab #3, due Tuesday, 9/20 (at start of class).

*NOTE: Next week Tuesday 9/18 there are no classes.*

- 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

- Are the two statements equivalent? September 27, 2022Let $X$ be any non-empty set Let $Y$ be any non-empty set Let $P(m,n)$ be any propositional statement containing object $m \in X$ and $n \in Y$ $[\forall\ m \in X,\forall\ n \in Y] [P(m,n)] \tag 1$ $[m \in X\ \wedge\ n \in Y] \Rightarrow [P(m,n)] \tag 2$ Is $(1)$ and $(2)$ logically equivalent? Why? […]Joe
- Determine the truth value of each of these statements (quantifier) September 27, 2022Let \begin{align*} A&=\{1,2,3,4,5,6,7,8,9,10\}, \\ B&=\{-5,-4,-3,-2,-1,0,1,2,3,4,5\},\\\ C&=\{-4,-3,-2,-1,0,1,2,3,4,5,6,8\}. \end{align*} Determine the truth value of these statements. $(\forall x \in A)(\forall y \in A)|x-y|\le 5$. $(\forall x \in A)(\exists y \in A)|x-y|\le 5$. $(\exists x \in A)(\forall y \in A)|x-y|\le 5$. $(\exists x \in A)(\exists y \in A)|x-y|\le 5$. $(\forall x \in B)(\forall y \in B)x+y=5$. $(\forall x […]Pitik Kepit
- Infer a set from its differences to other sets September 27, 2022There is a set $S$. We don't know the exact elements of $S$, but only know its cardinality $|S|$. Now we have some guesses to $S$, i.e., $\{ S_i \}_{i=1}^n$. For each $S_i$, we know its exact elements, and the cardinalities $|S_i \backslash S|$ and $|S \backslash S_i|$. The goal is to infer all the […]graphitump
- Does $\Sigma_1$-separation over $L_\alpha$ admissibility? September 27, 2022Inspired by the following tweet, I tried to prove the following statement: If $\alpha>\omega$ is a limit ordinal and $L_\alpha\models \Sigma_1\text{-Separation}$. Then $L_\alpha\models \mathsf{KP}$. The only axiom we need to verify is $\Delta_0$-Collection. Since $\langle L_\beta\mid\betaHanul Jeon
- Few questions regarding Proving logical Equivalence [closed] September 27, 2022I need help with a few questions. Also if you wouldnt mind providing the steps. Thanks:) 1.Use known logical equivalences to prove that (¬q ∧ p) ∧ ¬(q ∧ ¬r) is logically equivalent to ¬(p → q). 2. (a) Use known logical equivalences to prove that (¬p ∨ ¬q) → [(r ∧ q) ∧ p] […]sumone98
- Using double inclusion to show $(A △ B) ∪ C = (A ∪ C) △ (B \setminus C)$ September 27, 2022Could someone please tell me if I have used double inclusion correctly to prove $(A △ B) ∪ C = (A ∪ C) △ (B \setminus C)$? (NOTE: "$△$" denotes symmetric difference or exclusive or, i.e. $A △ B = (A ∪ B) \setminus (A ∩ B) = (A \setminus B) \cup (B \setminus A)$.) […]user51462
- How can I add an average function to a fragment of first order theory of arrays? September 26, 2022I am reading about decidability of first-order theories, concretely about arrays. I found the following decidable array property fragment (What's decidable about arrays?http://theory.stanford.edu/~arbrad/papers/arrays.pdf), which has a particular set of formulae and signature. Now, suppose I want to add an avg function to it: i.e., given an array of integers, it returns its average. Thinking in […]Theo Deep
- Are the converses of the following mentioned theorems also true? September 26, 2022Let $X$ be any non-empty set Let $Y$ be any non-empty set Let $P(m)$ be any propositional statement containing object $m \in X$ Let $Q(n)$ be any propositional statement containing object $n \in Y$ Let $R(m,n)=P(m)\ \wedge\ Q(n)$ Then we know that the following two Theorems are correct: First Theorem is the following: $\Bigg\{[\forall\ m […]Joe
- Express each of the following statements symbolically. September 26, 2022Let p and q denote the propositions p: The SAT verbal scores improved in this school district last year. q: The SAT math scores improved in this school district last year. Express each of the following statements symbolically. a. The SAT verbal scores and the SAT math scores improved in this school district last year. […]Kyanne Mae Corral
- Isomorphisms between extralogical signatures? September 25, 2022I am new to the study of mathematical logic. I have just finished reading the first three chapters of A Concise Introduction to Mathematical Logic by Wolfgang Rautenberg. I will try to formulate my question using Rautenberg's notation and terminology, although I am unsure how much of it is universal to the discipline and how […]Jason Swanson

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