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.
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.
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 $\neg A$.