# 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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### Optimal assignment for an unsatisfiable formula

Given an unsatisfiable formula $F$ in CNF, are there any methods to find an assignment that can satisfy as many clauses as possible?
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### Resolution Algorithms and one Example Problems?

We have a problem in one Resolution question. There is $5$ clauses, and want to prove the $6$th clause is true. which of the following clause is need more than one times to prove $6$th clause? $t$ ...
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### CNF Conversion and one $2015$ exam questions?!

if $\text{likes}(x,t)$ means that person $t$ likes food $x$, and $\text{food}(x)$ means $x$ is a food, $\text{CNF}$ of sentence "No food is liked by all person", and $F$ is Skolem function. The ...
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### Why does “if and only if” mean the exact same thing as “precisely when”?

The proposition "A precisely when B" states that A has the same truth value as B. The proposition "A if and only if B" states that A is true if B is true and that A is true only if B is true. ...
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### Prove that $(p \to q) \to (\neg q \to \neg p)$ is a tautology using the law of logical equivalence

I'm new to discrete maths and I have been trying to solve this: Decide whether $$(p \to q) \to (\neg q \to \neg p)$$ is a tautology or not by using the law of logical equivalence I have ...
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### Proving $(H \implies H) \implies G \quad \therefore \quad G$ using natural deduction [closed]

I'm stuck on this extra credit logic problem for my course... Prove $$(H \implies H) \implies G \quad \therefore \quad G$$ using methods of natural deduction. Any help would be ...
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### Negation of the definition of limit

A sequence $(x_n)$ of real numbers converges to a real number $x$ if For all $\epsilon> 0$ there exists a natural number $n_0$ such that for all $n \ge n _0$, $|x_n - x| < \epsilon$. ...
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### Discrete Mathematics - Quantifiers problem

This is a question from the Discrete Mathematics question from Kenneth Rosen book. I didn't understand the question and thus I am confused how to begin with question. Below is the question from the ...
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### Quantifiers Kenneth Rosen Discrete Mathematics

Please help me in regard with this question.I didn't have a clue how to solve this. The way I thought about this question is assuming the truth values of predicates P(x) and Q(x) and then trying ...
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### Proof of $(\neg A \supset A) \supset A$

As a (total) beginner in logic, I read this introduction : http://www.loria.fr/~roegel/cours/logique-pdf.pdf (in french). They give an exercise I couldn't achieve. Could someone help me (give an ...
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### Number of Minimally Functionally Complete (adequate) ternary Operators Sets and what they are

Is there a simpler way than through trial and error to determine the number of Minimally Functionally Complete Operator Sets (MFCOS) (or adequate operator sets) for a given arity and what those ...
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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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### 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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### 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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### 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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### 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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### 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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### 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 ...