5.4. Application of Resolution Rule

Try these first

1. 1.

   Define the resolution rule.

   Hint

   Think of it in terms of eliminating opposite literals.

2. 2.

   What is a resolvent?

   Hint

   It's what you get after resolving two clauses.

3. 3.

   What does the resolution rule achieve?

   • Eliminates literals
   • Derives new clauses
   • Confirms unsatisfiability

   Hint

   Focus on what action the rule facilitates.

4. 4.

   Resolution refutation demonstrates an argument is valid when it leads to the ___ clause.

   Hint

   Think about the nature of contradictions in logic.

5. 5.

   Prove the argument validity for the premises P → Q, Q → R, and premise P, conclude R using resolution refutation.

   Hint

   Focus on how each clause plays a role in resolution.

6. 6.

   Given a set of clauses: A ∨ B, ¬A ∨ C, ¬C, determine the validity of the argument A ∨ B implies C.

   Hint

   Analyze the interactions between the clauses effectively.