Questions tagged [conjunctive-normal-form]
A formula is in conjunctive normal form (CNF) if it is a conjunction of clauses, where a clause is a disjunction of literals.
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Ways to write CNF for an implication with disjunction?
I have the following statement before it's converted to CNF: p → (s ∨ q). When I initially convert this to a CNF, I get the following: ¬p ∨ (s ∨ q).
I'm wondering if I could use laws of associativity ...
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How to convert $(A \vee B) \wedge (C \vee D)$ to CNF?
Wikipedia states that all propositional logic statements can be transformed into CNF.
However, I'm not so sure how we can further simplify $(A \vee B) \wedge (C \vee D)$?
Or if this is CNF, why is it ...
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Calculus 1: Limits at negative infinity of quotients with square root, why introduce a negative when trying to simply
Why do we introduce a negative when trying to simplify? (circled in orange)
If x approaches -$\infty$ for both, the negative sign should cancel out..?
Khan acad's working:
Edit, removed my workings ...
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Why is $P \rightarrow Q$ equivalent to $\lnot P \vee Q$ in propositional logic CNF? [duplicate]
According to wikipedia, when we compute the CNF of propositional logic, we substitute $P \rightarrow Q$ with $\lnot P \vee Q$.
However, it seems to that when $P$ is False and $Q$ is True, then $P \...
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How to obtain the empty clause from CNF?
I have the following formula $\mathcal{F} = A(c, y) \wedge A(c, z) \wedge \neg E(c, z) \wedge \neg A(z, c)$ from which I've derived the clauses $\{A(c, y)\},\{A(c, z)\},\left\{\neg E\left(c, z_{1}\...
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Need help for turn this form $\neg ((p \Rightarrow q) \Rightarrow r)$ into DNF
How can I turn this form
$\neg( ( p \Rightarrow q ) \Rightarrow r )$
to disjunctive normal form and to the disjunctive normal form fully developed ?
I have done the truth table see below
I ...
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How can I find the CNF of ($A$ and $B$ or $C$) and ($B$ or not $C$) using a Karnaugh map?
$$(A\land B \lor C) \land (B \lor \lnot C)$$
I know how to create the truth table and Karnaugh map of a logic expression. But I couldn't find exactly how to calculate the simplified CNF of it using ...
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What is the conjunctive normal form for $(\neg Q\land P) \lor (\neg Q\land R) \lor (\neg P \land \neg R)$
$(\neg Q\land P) \lor (\neg Q\land R) \lor (\neg P \land \neg R)$
i have calculated this using wolframalpha and the output of CNF was $(\neg Q \lor\neg P) \land (\neg Q \lor\neg R) $
but all i ...
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Conjunctive Normal Form evaluates true when atleast half of the clauses are true.
This is an Exam question.
Which of the Following is TRUE about formulae in Conjunctive Normal form?
-For any formula, there is a truth assignment for which at least half the clauses evaluate true.
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Simplify the given boolean expression into the "Canonical Conjunctive Normal Form“.
Simplify the boolean expression, into the “Canonical Conjunctive Normal Form":
$$x_0\overline{x_0} + x_1\overline{x_1} + \overline{x_2}+x_3$$
Here's my attempt:
$$\begin{align}
x_0\overline{x_0} ...
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CNF and DNF form of single logical variable
I am learning boolean algebra. So apologies for this naive question. During our discussion among friends, we came across following puzzle,
How can I convert following statement into CNF and DNF?
$$ ...
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First order logic translation from the sentence "Nobody who loves every dog loves any armadillo."
i'm new to first order logic and i'm having some confusion with translating the sentence above.
My solution for the sentence is :
∀x ∀y ∀z ((DOG(y) ∧ LOVES(x, y) ∧ ARMADILLO(z)) → ¬LOVES(x, z)) (1)
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First Order Logic: How to transform to prenex conjunctive normal form and Skolem form?
This is the sentence that needs to be transformed: ∃x∀y(Ax → (Bxy ∨ ¬Cy)) → ∀x∃y(Py → Qyx)
I have gotten to the point where I eliminated all occurrences of → and imported all negations inside all ...
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CNF-SAT is NP-complete if and only if CNF-UNSAT is co-NP-complete?
I have shown that a language $A$ is NP-complete $\iff$ its complement $\overline{A}$ is co-NP-complete.
Also, I have shown that CNF-SAT is NP-complete.
Since UNSAT is the complement of SAT, then ...
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CNF unsatisfiability NP-complete?
I have two problems, CNF-SAT and CNF-UNSAT, that decide if a formula $\phi$ on Conjunctive Normal Form is satisfiable and unsatisfiable, respectively. I have already shown that CNF-SAT is $NP$-...
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