Finding a logically equivalent conjunctive normal form. 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 $A\land (\lnot B\lor \lnot A)\land C$?

Conditional Negation, Distribution, Complementation, and Identity.

$\begin{align} &\
eg (A\to B)\vee(\
eg A\wedge C)\\\\\equiv ~& (A\wedge\
eg B)\vee(\
eg A\wedge C)\\\\\equiv~& (A\vee\
eg A)\wedge(A\vee C)\wedge(\
eg B\vee \
eg A)\wedge(\
eg B\vee C)\\\\\equiv~& \qquad\qquad\quad(A\vee C)\wedge(\
eg B\vee \
eg A)\wedge(\
eg B\vee C)\end{align}$

I am not sure how you figured this would be equivalent to $A\wedge(\
eg B\vee\
eg A)\wedge C$, because it is not.