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Thread: I tried to make Sentence to CNF Format but I am not sure that is correct

  1. #1
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    I tried to make Sentence to CNF Format but I am not sure that is correct

    Hi ,

    I would very happy if someone could check please if I do the exercise correctly , I will upload here image .
    I don't know to solve this with True/False Table and from there to change the format to CNF , I do this task only with Basic Formulas to get to CNF Pattern ,

    I tried to make Sentence to CNF Format but I am not sure that is correct-cnf.jpg


    Thanks for helping .
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  2. #2
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    Re: I tried to make Sentence to CNF Format but I am not sure that is correct

    Grinding out the truth table makes it look like the answer is just TRUE.
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    Re: I tried to make Sentence to CNF Format but I am not sure that is correct

    Quote Originally Posted by MathPro17 View Post
    True/False Table and from there to change the format to CNF , I do this task only with Basic Formulas to get to CNF Pattern ,
    Click image for larger version. 

Name:	CNF.JPG 
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    HERE is the truth-table.
    It shows a tautology.

    $ \begin{align*}(A \to (B \to C)) \to ((A \to \neg C) \to (A \to \neg B))& \equiv (\neg A \vee (\neg B \vee C)) \to ((\neg A \vee \neg C) \to (\neg A \vee \neg B))\\& \equiv \neg (\neg A \vee (\neg B \vee C)) \vee (\neg (\neg A \vee \neg C) \vee (\neg A \vee \neg B))
    \\& \equiv (A \wedge B \wedge\neg C) \vee (A \wedge C) \vee (\neg A \vee \neg B) \end{align*}$

    HERE is that truth-table.
    Last edited by Plato; May 8th 2018 at 12:26 PM.
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    Re: I tried to make Sentence to CNF Format but I am not sure that is correct

    Your very first step is wrong P->Q is equivalent to P V ~Q, not P V Q.
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    Re: I tried to make Sentence to CNF Format but I am not sure that is correct

    Quote Originally Posted by HallsofIvy View Post
    Your very first step is wrong P->Q is equivalent to P V ~Q, not P V Q.
    Can you show all of us what first step that occurs within the PO?

    In fact that is wrong. $\large{(P\to Q)\equiv(\neg P\vee Q)}$
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    Re: I tried to make Sentence to CNF Format but I am not sure that is correct

    Hi,

    Thanks for all your help ,
    I have question about this : "≡(A∧B∧C)∨(A∧C)∨(A∨B)"
    the CNF mean Sentence with : (something) ∨ ( something ) ∨ ( something ) . it is Okay to leave this ( Something ) that hasn't "∧" or " " there are
    "∨' OR I split this like this : ≡(A∧B∧C)∨(A∧C)∨(A)∨(B) , Is It Right ?

    Thanks for all.
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    Re: I tried to make Sentence to CNF Format but I am not sure that is correct

    Quote Originally Posted by MathPro17 View Post
    I have question about this : "≡(A∧B∧C)∨(A∧C)∨(A∨B)"
    the CNF mean Sentence with : (something) ∨ ( something ) ∨ ( something ) . it is Okay to leave this ( Something ) that hasn't "∧" or " " there are "∨' OR I split this like this : ≡(A∧B∧C)∨(A∧C)∨(A)∨(B) , Is It Right ?
    Irving M. Copi is considered as the authority on symbolic logic in the 20th century. Here is what he wrote: "A statement is in conjunctive normal form when in addition to statement variables it contains no symbols other than those for conjunction, disjunction, or negation and negation symbols are applied only to statement variables"..

    Do you see how that applies to my solution?
    BTW: according to Copi one would not need to use $(\neg A)$ for $\neg A$.
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