# Math Help - Causal form

1. ## Causal form

What is the causal form of ((p ⇒ q) ⇒ (p ⇒ r))
And the negation of the result?

2. ## Re: Causal form

Do you mean clausal form, i.e., a conjunctive normal form?

What have you tried to find it, and what exactly is your difficulty?

3. ## Re: Causal form

(p=>q)=>(p=>r)
(¬pvq)=>(¬pvr)
¬(¬pvq)v(¬pvr)
(p^¬q)v(¬pvr)
.
And here is where I'm not sure.

With the result I have to negate it because is a conclusion to include in a Resolution, and I'm not sure again of the result.

4. ## Re: Causal form

Originally Posted by doctorpi
(p=>q)=>(p=>r)
(¬pvq)=>(¬pvr)
¬(¬pvq)v(¬pvr)
(p^¬q)v(¬pvr)
.
And here is where I'm not sure.
At this point, use distributivity laws.

[(p ∧ ¬q) ∨ ¬p] ∨ r
[(p ∨ ¬p) ∧ (¬q ∨ ¬p)] ∨ r
¬q ∨ ¬p ∨ r

Originally Posted by doctorpi
With the result I have to negate it because is a conclusion to include in a Resolution, and I'm not sure again of the result.
The negation is q ∧ p ∧ ¬r.