# 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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### how to prove the following formula via natural deductions $a ∧ ¬a \vdash b ∧ ¬b$

Hi I am trying to prove the following formula via natural deduction and this is what I have so far. I am not sure however if this is entirely correct. If I could get some verification and be pointed ...
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### Tautology example [closed]

How to verify if this logical statement is a tautology? AB+BCD+AC=NOT(AB+AC) I have seen all the posibilities but I am not sure that is tautology. And I have to solve it and to do all the ...
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### Generating all logic propositions

I'm looking for a way of generating all logic propositions (propositional calculus) in an "algorithmic" way. The equivalence is symbolic, so $\neg\neg a \neq a$ and $\neg a \lor b \neq a \implies b$, ...
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### Prove Tautology

Can you please prove the equation (~pVr)^(pVq)->(qVr) without using truth table. I have tried and ended up half way ~[(~pVr)^(pVq)]V(qVr) ~(~pVr)V~(pVq)V(qVr) (p^~r)V(~p^~q)VqVr (p^~r)VrV(~p^~q)Vq
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### How to specify the corresponding line of a truth table in a formula?

How to specify the corresponding line of a truth table in a formula: $$p \to (\neg q \lor (q \to p))$$ $p$ evaluates to $F$ and $q$ evaluates to $T$. I want to know the method followed to find this....
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### How to handle degrees (numerical attributes) in logic? How to model “quantitative changes lead to qualitative changes”?

I am using logics (propositional, predicate, modal) to model one domain, but there are variables that have non-boolean domains, these variables are degrees (it is sufficient that they are degrees, ...
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### What will the declarative sentence No shoes, no shirt, no service be in propositional logic?

I need to write the following declarative sentence in propositional logic. No shoes, no shirt, no service. My solution is: ~p,~q, ~r , is it correct or do i need to use implication -> instead
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### All hill-stations have a lake. Ooty has two lakes?

All hill-stations have a lake. Ooty has two lakes. Which of the statement(s) below is/are logically valid and can be inferred from the above sentences? $(i)$ Ooty is not a hill-station. $(ii)$ No ...
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### Propositional Resolution - How to prove?

I was given the following argument which is valid. I must prove it using propositional resolution. ((A $\rightarrow$ B) $\rightarrow$ C) (C $\rightarrow$ (D · E)) $∴$ (B $\rightarrow$ D). So ...
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### Solving rules of inference questions from Discrete Maths Rosen and I am confused on a step

So the question is, Show that the premises “It is not sunny this afternoon and it is colder than yesterday,” “We will go swimming only if it is sunny,” “If we do not go swimming, then ...
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### Consistency of a Knowledge base (resolution)

To prove Q is a logical consequence of a knowledge base KB, it is possible to add not(Q) to KB and perform resolution, and reach an empty clause. But how is it possible to show Q is not a consequence ...
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### Logical Equivalence as an equivalence relation

I've been given the following problem for homework and I'm struggling with where to begin "Suppose we have a set of 5 propositional variables, denoted L. By considering logical equivalence, what is ...
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### Show that a set of logical connectives is expresively complete

I've been trying to figure this out for hours now, there doesn't seem to be ample resources online for my skill level to solve such a question: Show that a set of connectives {∧,¬} is expressively ...
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### substitutional interpretation of quantifiers: examples?

About the differences between propositional logic and (first order) predicate logic, given that if my basis is propositional logic I have to substitute the universal and existential quantifiers with ...
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### Propositional logic vs predicate logic: examples?

About the difference between the propositional logic and the (first order) predicate logic-> can you give me one or more remarkable examples which underly the differences and the similarities ...