Prove the following proposition using resolution.

Question

Prove the following proposition using resolution.

[(p → q) ∧ (q → r) Λ p] → r

 

Show first the conjunctive normal form of the negation of the proposition. Then show a sequence of numbered clauses where each clause should either be marked as a premise or a result from resolution of two identified former clauses. Stop when you get a clause that proves what needs to be proven.

Answer 1

(p→q)∧(q→r)∧p →

(¬p∨q)∧(¬q∨r)∧p →

(¬p∨r)∧p→

r

 

the reasons for the above lines are (not in the right order!):

disjunctive syllogism

resolution

given

logical equivalence

 

can you put them in the right positions?

 

Any questions comment back. Dr. F