5.1. Lecture -05

Try these first

1. 1.

   What is the resolution rule and how is it applied?

   Hint

   Think about the process of cancellation.

2. 2.

   Define what a resolvent is.

   Hint

   It involves two original clauses.

3. 3.

   What does the resolution rule allow in logic?

   • Only cancellation
   • Deriving new conclusions from clauses
   • Summarizing information

   Hint

   Think about resolving two clauses.

4. 4.

   True or False: A resolvent contains a common literal.

   • True
   • False

   Hint

   Recall the process of resolving clauses.

5. 5.

   Given the clauses C1 = A ∨ B, C2 = ¬A ∨ C, and C3 = ¬C, can you apply resolution to derive the conclusion? Demonstrate your reasoning.

   Hint

   Focus on resolving pairs step by step.

6. 6.

   Demonstrate the proof by resolution refutation for premises: P → Q, Q → R, and the conclusion ¬R.

   Hint

   What negation do you need to add?