I have been trying to do this all day but I am not getting anywhere with it, could anyone help me?
My formula is
r → (p ↔ ¬q)
And I want to convert it into CNF
When I do it, I get this answer, which does not seem correct:
(Q ∨ P ∨ ¬R) ∧ (¬P ∨ ¬Q ∨ ¬R)
That is correct.
Suppose $(Q ∨ P ∨ ¬R) ∧ (¬P ∨ ¬Q ∨ ¬R)$ and assume $R$. The assumption and supposition can both be satisfied when $P$ and $\lnot Q$, or when $\lnot P$ and $Q$ are satisfied: thus $R\to(P\leftrightarrow\lnot Q)$
Suppose $R\to(P\leftrightarrow\lnot Q)$. This is satisfied when $R$ is falsified or $P\leftrightarrow\lnot Q$ is satisfied. The later is satisfied at least one from $P,Q$ is satisfied and at least one is falsified. This: $(\lnot R\lor P\lor Q)\land(\lnot R\lor\lnot P\lor\lnot Q).$