Here is the definition of a conjunctive normal form:
A conjunctive normal form is a conjunction of one or more conjuncts that are disjunctions of one or more literals (letters). For example, $A \land (B \lor A) \land (\lnot B \lor A)$ is a conjunctive normal form.
I need to find a logically equivalent conjunctive normal form of the expression $\lnot (A \to B) \lor (\lnot A \land C)$. The answer in the textbook is $(A \lor C) \land (\lnot B \lor \lnot A) \land (\lnot B \lor C)$. I don't understand how they got this answer.
Can another answer be $A\land (\lnot B\lor \lnot A)\land C$?
Best Answer
Conditional Negation, Distribution, Complementation, and Identity.
$\begin{align} &\neg (A\to B)\vee(\neg A\wedge C)\\\equiv ~& (A\wedge\neg B)\vee(\neg A\wedge C)\\\equiv~& (A\vee\neg A)\wedge(A\vee C)\wedge(\neg B\vee \neg A)\wedge(\neg B\vee C)\\\equiv~& \qquad\qquad\quad(A\vee C)\wedge(\neg B\vee \neg A)\wedge(\neg B\vee C)\end{align}$
I am not sure how you figured this would be equivalent to $A\wedge(\neg B\vee\neg A)\wedge C$, because it is not.