# Finding CNF of $(p \rightarrow q) \rightarrow p$ and $\lnot (q \wedge (\lnot p \rightarrow q))$

I'm trying to find the CNF of the $$(p \rightarrow q) \rightarrow p$$ and $$\lnot (q \wedge (\lnot p \rightarrow q))$$, and afterwards proving it's validity. As i'm new to CNF i wanted to ensure i've found the right CNF before trying to move on, so for $$(p \rightarrow q) \rightarrow p$$:

the normal from is: $$p \rightarrow q \wedge q \rightarrow p$$

and it's valid?

• The CNF shouldn't contain the "$\rightarrow$" operation – HEKTO Dec 3 '18 at 23:03

$$(a_1 \vee \neg a_2 \vee \dots \vee a_n) \wedge (\neg b_1 \vee \dots \vee b_m) \wedge \dots \wedge (c_1 \vee \dots \vee c_l)$$
therefore a formula in CNF has only literals (i.e. atoms or negated atoms), $$\wedge$$, and $$\vee$$. It doesn't have $$\to$$.
If it's allowed to transform $$p \to q$$ to its equivalent formula $$(\neg p) \vee q$$, you can use this for the first step to convert a given formula to a CNF formula.