5.2. Resolution

Try these first

1. 1.

   What is the resolution rule?

   Hint

   Remember how common literals work in clauses.

2. 2.

   Define a tautology.

   Hint

   Think about logical statements that don't change in truth.

3. 3.

   What does the resolution rule allow us to do?

   • A) Disprove an argument
   • B) Simplify and create new clauses
   • C) Verify tautologies

   Hint

   Think about the mechanics of how clauses interact.

4. 4.

   True or False: The conclusion of a valid argument must be a tautology.

   • True
   • False

   Hint

   Consider what valid means in terms of premises.

5. 5.

   Given the clauses A: (p ∨ ¬q), B: (¬p ∨ r), and C: (¬r), demonstrate using resolution that q must be true.

   Hint

   Look for literals that can be paired effectively.

6. 6.

   Construct a set of clauses that are satisfiable and then show how their resolution can lead to the conclusion being false.

   Hint

   Explore combinations of true and false assignments.