5. Discrete Mathematics

Try these first

1. 1.

   What is a clause?

   Hint

   Think about how clauses are formed.

2. 2.

   Define a literal in the context of logic.

   Hint

   Remember the types of variables in logical expressions.

3. 3.

   What does the resolution rule allow us to do?

   • Conclude from clauses
   • Define literals
   • Assign truth values

   Hint

   Think of how we combine different statements in logic.

4. 4.

   True or False: An unsatisfiable set of clauses means they can all be true at the same time.

   • True
   • False

   Hint

   Consider the definition of contradiction.

5. 5.

   Construct a proof by resolution refutation for the premises P, ¬P ∨ Q, Q → R, and show that the argument is valid or invalid.

   Hint

   Focus on how negating conclusions can lead to contradictions with premises.

6. 6.

   Given clauses A ∨ B, ¬A, and C, derive the resolvent and conclude whether the set is satisfiable.

   Hint

   Look for common literals to resolve.