I have the following statement before it's converted to CNF: p → (s ∨ q). When I initially convert this to a CNF, I get the following: ¬p ∨ (s ∨ q).
I'm wondering if I could use laws of associativity and commutativity to rearrange this statement a bit more while keeping it in the CNF.
Using the associativity law, we can say that ㄱp ∨ s ∨ q is equivalent to s ∨ ㄱp ∨ q.
Using the commutativity law, ㄱp ∨ s ∨ q is equivalent to s ∨ ㄱp ∨ q.
Alternatively, could another way to express this statement above be ㄱs ∨ p ∨ q? If not, what is the correct way to express it? I am trying to conduct a proof by resolution, and my goal right now is to keep the CNF while getting some sort of negation of s. I want to know if this is a valid way of rewriting the original statement.