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Mathematics

Questions tagged [propositional-calculus]

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Appropriate for questions about truth tables, conjunctive and disjunctive normal forms, negation, and implication of unquantified propositions. Also for general questions about the propositional calculus itself, including its semantics and proof theory. Questions about other kinds of logic should use a different tag, such as (logic), (predicate-logic), or (first-order-logic).

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3votes
1answer
74views

In propositional logic, the "semantics" $v[\![\varphi]\!]$ of a formula $\varphi$ with respect to some valuation $v$ is defined inductively on the syntactic structure of the formula $\varphi$...
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The task is to show that:$\forall p F \to G$ is not equivalent to $\exists p(F \to G)$ where F and G are propositional formulas.I'm aware that when applying prenex rules to a formula to transform a ...
2votes
1answer
96views

A := It rains.B := I should pick an unbrella.It rains, therefore I should pick an umbrella.p1) Ac) BConsider the above premise and conclusion. Initially I'd ...
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An argument has premises $p$ and one conclusion $c$. Can I write the argument as $p \to c$, in the form of Material conditional?What are the differences between arguments and material conditionals?...
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I’m working on a logic and combinatorics problem about arranging a teacher’s Monday schedule.The schedule has four sessions (1, 2, 3, 4) and four subjects: Mathematics (M), Biology (B), Geography (G),...
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In propositional logic: isn't the RAAD equivalent to what the definition of the material conditional implies? As in the material conditional both Q = 0 and Q = 1 signifiy a true formula when the ...
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The truth table of the IF operator is shown in the above.Let p be "a number $n$ is even" and q be "a number $n$ is divisible by 2"Then If p then q evaluates to true if both ...
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I was playing the excellent math game "The Incredible Proof Machine", which is a tutorial of sorts on formal proofs using a block-based, flowchart-style system of logical inferences. One of ...
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Let $V(p, c)$ mean that person $p$ has visited country $c$ in the world.Is the following deconstruction correct?Someone has visited every country in the world except Libya.There is a person $p$ ...
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1answer
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Negation Laws shown in Table-6 here are stated as:$$p ∨ ¬p ≡ \mathbf{T} \text{ and } p ∧ ¬p ≡ \mathbf{F}$$Is it same as the Law of Excluded Middle? This gets confusing for a novice like me when same ...
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In the book Gödel's Theorems and Zermelo's Axioms by Halbeisen and Krapf the first chapter contains an excercise that asks us to prove$$\phi\rightarrow \psi \vdash \neg \psi \rightarrow\neg \phi,$$i....
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I recently took an introductory logic course (I am a philosophy student) and on the final exam one of the questions asked me to draw up a truth-table for $( ( \alpha \to \beta ) \wedge ( \neg \alpha \...
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I'm reading A Course in Mathematical logic and Computability Theory by Gerasimov and for the exercise the book asks the question to prove the following statement in Hilbert proof system:$$A,\lnot B \...
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3votes
1answer
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I'm trying to learn category theory and in my adventures reading Borceux's "Handbook of Categorical Algebra 2", I encountered the following definition:A presentation of an algebraic theory ...
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The last task in Session 5 of the Incredible Proof Machine(a tool to perform proofs in various logics visually) is to prove $A\land(B\to\perp)$ when given $(A\to B)\to\perp$, in which capitals ...

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