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

1. ## 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 ,

Thanks for helping .

2. ## 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.

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

Originally Posted by MathPro17
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 ,
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.

4. ## 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.

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

Originally Posted by HallsofIvy
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. $\large{(P\to Q)\equiv(\neg P\vee Q)}$

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

Hi,

Thanks for all your help ,
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.

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

Originally Posted by MathPro17
BTW: according to Copi one would not need to use $(\neg A)$ for $\neg A$.