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Handouts – content-related handouts distributed in class

Assignments – OpenLab assignments

Exam Reviews – review sheets and answer keys for in-class exams and final exam

- Which statement is not a mistake that Reina has made? July 13, 2024"A survey done at a certain high school found that any student who liked tennis also liked swimming. They also found that students only liked swimming if they could swim." Reina: If 30 students from the high school can swim, then 30 students from the school also like tennis. If the quoted paragraph above is […]Bacterigerm
- Foundations of Math - Algebraic Logic [closed] July 12, 2024Has there been any recent work using algebraic logic as opposed to set theory or homotopy type theory for a foundation of mathematics?Justify
- Number of lattices over a finite set July 12, 2024I'm interested in finding a general formula for the number of lattices possible over a finite set $S$ as a function of the set's cardinality. For instance, how many lattices over $\{1, 2, 3\}$ are there? Since the set contains three elements, and a lattice is a partial order, we must count the number of […]lafinur
- Is there a propositional proof system that is not known to be simulated by extended Frege? [closed] July 12, 2024Extended Frege is a propositional proof system that is achieved by adding the extension rule to a Frege system. That rule allows to replace formulas with fresh variables. A propositional proof system $P$ is said to simulate a propositional proof system $Q$ if for every proof in $Q$ of length $|x|$, $P$ has a proof […]rus9384
- Proving the Negation of a Formula does not Require the Formula as an Assumption July 12, 2024The following lemma states that if we can prove negation of a Well Formed Formula (WFF) $\alpha$ by assuming the formula itself, then we can do it without such an assumption. Lemma. Let $\Sigma$ be a set of WFFs and $\alpha$ a WFF. If $\Sigma \cup \{\alpha\} \vdash (\neg \alpha)$, then $\Sigma \vdash (\neg \alpha)$. […]Hosein Rahnama
- A property of $\lt$ in Primitive recursive arithmetic July 11, 2024In Primitive recursive arithmetic (PRA), we can introduce $\lt$ by introducing its representing function $K_{\lt}$, where $K_{\lt}(x,y) =sg(x+1-y)$. Here "sg" and "-" are the functions defined by $sg(0)=0\land sg(x+1)=1$, $pred(0)=0\land pred(x+1)=x$ and $a-0=a\land a-(b+1)=pred(a-b)$. In this situation, I want to prove in PRA that if $K_{\lt}(x,y+1)=0$, then $K_{\lt}(x,y)=0\lor x=y$. If $K_{\lt}(x,y+1)=0$, then $sg( (x+1)-(y+1))=sg(pred(x+1-y))=0$. Note […]nilpotent
- First-Order Logic With Extensional Set Membership July 11, 2024It is common to sometimes present First-Order Logic with equality and sometimes without. Adding equality has some nice benefits, including the ability to talk about some number of things, e.g. $\exists x \forall y (A(y) \leftrightarrow y=x)$ is enough to capture “exactly one thing is $A$.” Given that, is there any use to going a […]PW_246
- Paradox in Prisoner's dilemma July 11, 2024I have come across a curious paradox concerning The Prisoner's Dilemma Suppose 4 things : prisoners A and B are rather stupid people and decide to use an artificial intelligence program to decide through a logical proof whether it is better to cooperate or defect. the AI program is deterministic both prisoners use the same […]Arnaud
- in definition of assigment, what's means 'except possibly a'? July 11, 2024in frist-order logic, part of assignments practice represent like this "if 𝜙is ∀𝛼𝜓, where 𝛼 is a variable, then ⊨vℳ 𝜙 iff for every assignment 𝑣' that agrees with 𝑣 on the values of every variable except possibly 𝛼, ⊨v'ℳ'𝜓 " here I don't understand except possibly 𝛼, because I understand 'for all x...' means […]유준상
- Prove: Let α be a proposition containing only Boolean connectives ∧,∨. Then any assignment satisfying α must also satisfy f(α) July 10, 2024The question: Let f be a mapping that takes as input a Boolean proposition (no quantifiers) and outputs the same proposition but with all ∧ symbols replaced by ∨. For example: $$ f(x_1 ∧ (x_2 → ¬x_5) = (x_1 ∨ (x_2 → ¬x_5) $$ Prove: Let α be a proposition containing only Boolean connectives ∧,∨. […]User33975329257439645

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