What is the causal form of ((p ⇒ q) ⇒ (p ⇒ r)) And the negation of the result? Thanks in advance,.
Last edited by doctorpi; Apr 17th 2013 at 02:30 PM.
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Do you mean clausal form, i.e., a conjunctive normal form? What have you tried to find it, and what exactly is your difficulty?
(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.
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.
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