Tag: calculus
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- For each of the following sets, determine whether 2 is an element of that set: {{2},{{2}}} October 5, 2024{{2},{{{2}}} I think that 2 belongs to {2} (because has the element 2). But 2 has no elements in {{2}} (because the only element that explicitly possesses is {2}, no the element 2 itself). Am I right?PEREZ MONSIVAIS JOSE DE JESUS
- Universal quantifier over disjunction in intuitionistic logic October 5, 2024I have a question about the following sequent, valid in classical logic: $$\forall x [\phi(x) \vee \psi] \vdash \forall x [\phi(x)] \vee \psi$$ Importantly, we assume $\psi$ does not contain any free $x$. Is this sequent valid also in intuitionistic logic? The converse sequent is not hard to prove, but with this direction I am […]Tony Dolezal
- Truth-tabling $\left[\,(p\lor q)\land(p\to r)\land(q\to r)\,\right]\implies r $ [duplicate] October 5, 2024Our professor assigned this homework. By constructing a truth table, prove this logical implications: $$\left[\,(p\lor q)\land(p\to r)\land(q\to r)\,\right]\implies r $$ How to handle two AND's in one bracket?Alix
- can self-referential statements be regarded as statements(propositions)? [closed] October 5, 2024By definition, a proposition (statement) is a declarative sentence that is either True or False, but not both. Hence the question, is a referential statement, such as "This sentence is false" can be regarded as a statement? BestBurakhan Aksoy
- "Every Cat loves its mother or father" October 5, 2024"Every Cat loves its mother or father" $\forall x ( \operatorname {Cat}(x) \land (\operatorname {Loves}(x,\operatorname{Mother}) \lor \operatorname {Loves}(x,\operatorname {Father}) )$ Although I know that a universal quantifier cannot be used with conjunction (not because of syntax error), I have issues understanding why the above translation is incorrect. I mean, it does sound correct: for every […]dikshank
- The logic subtlety behind solving differential equations. October 5, 2024Let me first explain what has led me to ask this question. When solving functional equations, it is often the case that through a link of implications (that is, uni-directional implications), we get several possible solutions for the functional equation. Then, we have to plug these functions into the original equation to see whether each […]The_Eureka
- Possible Error in Poizat's A Course in Model Theory (Chapter 7, Arithmetic) October 4, 2024I was reading Chapter 7 on Arithmetic in Bruno Poizat's A Course in Model Theory and noticed a potential error in Section 7.1 regarding the axioms defining the successor function. The axiom is given as: ($\forall x) (x \neq 0)$ This seems incorrect since it should express that 0 is not the successor of any […]Jackson Willoughby
- "All countries that border Ecuador are in South America" October 4, 2024Parts (i) and (iv) make sense as they are obvious. Part (ii) says "for every C, if that is a country, then, if it borders Ecuador then it is in SouthAmerica." I want to know whether there is a method to convert "and ($\land$)" to implication; this way, parts (i) and (ii) are interchangable. I […]dikshank
- Prove that a translation is (or is not) essentially surjective October 4, 2024Let $L_1$ be a first-order language with only one extralogical symbol, i.e. a unary predicate $Px$. Let $L_2$ be a first-order language with only one extralogical symbol, i.e. a binary predicate $Rxy$. Let $T_1$ be the empty theory, i.e. $T_1= \emptyset$. Let $T_2$ be a theory that just says that $R$ is symmetric: $T_2 = […]Soennecken
- “Richard’s brothers are John and Geoffrey” October 4, 2024From Chapter 8 of the book Artificial intelligence: The modern approach: “Richard’s brothers are John and Geoffrey”: Brother (John, Richard) $∧$ Brother (Geoffrey, Richard) $∧$ John $\neq$ Geoffrey $∧$ ∀x Brother (x, Richard) ⇒ (x=John $∨$ x=Geoffrey) Isn't translation this simpler, with the exact same meaning? If not, what is wrong with it? ∀x Brother […]dikshank
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