Is this CNF equivalent correct?

Question

I am reading Wolf’s A Tour Through Mathematical Logic. In Section 1.2, Propositional Logic, he gives the following example:

Example 6. The statement $ \mathsf{[(P\rightarrow\neg Q)\leftrightarrow (R\vee\neg P)]}$ has the same conjunctive normal form equivalent $$\mathsf{[(P\vee Q\vee R)\wedge (\neg P\vee Q\vee R)\wedge (\neg P\vee\neg Q\vee\neg R)]}.$$

I don’t think it is correct.

Answer 1

You are right. The formula $(P \rightarrow \neg Q) \leftrightarrow (R \vee \neg P)$ is true whenever $P$ is false. The given CNF, however, is false when $P$, $Q$, and $R$ are all false.

A little algebra shows that the given formula is equivalent to

$$ \neg P \vee (Q \leftrightarrow \neg R) $$

or, in CNF,

$$ (\neg P \vee Q \vee R) \wedge (\neg P \vee \neg Q \vee \neg R) \enspace. $$