3.3. Unsatisfiable Proposition

Try these first

1. 1.

   Define a satisfiable proposition.

   Hint

   Think about what it means for something to be true.

2. 2.

   Give an example of a tautological statement.

   Hint

   Consider statements that cover all possibilities.

3. 3.

   What is a satisfiable proposition?

   • A proposition that is always false
   • A proposition that is true at least once
   • A tautology

   Hint

   Think about what it means for an expression to be true in logic.

4. 4.

   Is 'p and not p' satisfiable?

   • True
   • False

   Hint

   Consider the logic of contradiction.

5. 5.

   Prove whether the proposition 'A or (B and not B)' is satisfiable or unsatisfiable.

   Hint

   Look for truth assignments for each variable.

6. 6.

   Convert the equivalent of '(p and q) implies r' to CNF.

   Hint

   Apply implications and understand distribution rules.