3.7. Clause and Literal Definitions

Try these first

1. 1.

   Define a satisfiable proposition.

   Hint

   Think about conditions under which a proposition can be true.

2. 2.

   What is a clause?

   Hint

   Consider how literals group together.

3. 3.

   Can a proposition be satisfiable if it is always false?

   • True
   • False

   Hint

   Remember the definition of unsatisfiable propositions.

4. 4.

   What is CNF?

   • A disjunction of clauses
   • A conjunction of clauses
   • A single literal

   Hint

   Think about how logical expressions are structured.

5. 5.

   Given the logical expression (p OR q) AND (¬r OR s), show how to convert it into CNF.

   Hint

   Check for disjunctions within conjunctions.

6. 6.

   Create a satisfiable and an unsatisfiable proposition and explain why they fit the definitions.

   Hint

   Remember the definitions and look for conflicts.