Tagged Questions

Questions about truth tables, conjunctive and disjunctive normal forms, negation, and implication of unquantified propositions would fit very nicely under this tag. Questions about other kind of logics should be tagged with [logic] instead.

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What would be the solution to this logic puzzle? [on hold]

This is the puzzle I am having trouble in understanding Also, do explain me the question along with the answer. Thank You
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Notation: When to imply and when to express equivalence?

I have recently been trying to improve the readability of my work as I solve equations, so that I and others can easily navigate how exactly I solved them. I want to make sure I using proper notation. ...
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Is it possible to eliminate a contradiction without recourse to the principle of explosion?

I'd like to derive the following inference rule: $$\frac{p\lor(q\land\neg q)}{p}\quad\text{[ContradictionElimination]}$$ I assumed that I could do this minimally somehow, however it turns out I ...
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Solving Logical equivalence & propositional logic problems without truth tables

I have no particular "Logic question" in hand at the time being, but need help to understand a way that can be used to prove "Logical equivalence without using truth tables". moreover can we solve ...
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Is there a name for the propositional tautology (and it's associated rule) $Q\Rightarrow(P\Rightarrow Q)$?

I have the tautology $Q\Rightarrow(P\Rightarrow Q)$. I can prove this intuitionistically: ...
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What exactly is the role of the material conditional in intuitionistic logic?

There seems precious little around about the use of the material conditional in intuitionistic logic aside from the Wikipedia page https://en.wikipedia.org/wiki/Material_conditional and I can't seem ...
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Encoding a graph coloring problem in SAT/CNF for DPLL algorithm

I'm having trouble trying to convert the following problem to SAT for later application to DPLL: Given a connected, undirected graph G, with k colors $\{ c_1 , ..., c_k \}$ and any number of ...
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Is double negation introduction an axiom of intuitionistic logic or can it be derived?

If I have a rule for negation introduction... Rule (NegationIntroduction,ProofByNegation) Premises P=>Q, P=>⌐Q Conclusion ⌐P ...then it seems ...
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Proving existence of a wff that is logically equivalent to a wff given some conditions

For convenience, let us define a wff to be positive if there is no use of the negation symbol $\neg$ at all in the wff. Hence, for example, $W=P\iff Q$ is a positive wff. Now the question is to show ...
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Propositional logic for a proof

I was able to prove the following proposition Suppose that $x > 0$ and that $y \in [0, 1] \cap S_x$. Then $$y \in [c(x), d(x)],$$ where $c(x)$ and $d(x)$ are two particular real valued ...
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How many equivalence classes are there under the relation of logical equivalence?

I was wondering how might one go about solving the question: How many different last columns occur among all the truth tables with propositional variables p, q, r, s? (In other words, how many ...
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Are these two logical statements equal?

I found this question from a website: "Neither the fox nor the lynx can catch the hare if the hare is alert and quick." Let: P: The fox can catch the hare Q: The lynx can catch ...