7.8. Final Question

Try these first

1. 1.

   What is a functionally complete set of logical operators?

   Hint

   Think about the operators you commonly use.

2. 2.

   Convert the expression p → q to an expression using only negation and disjunction.

   Hint

   Use the implication identity.

3. 3.

   What is the definition of a functionally complete set of logical operators?

   • A set that can express some logic statements.
   • A set that can express every logical statement.
   • A set that is always true.

   Hint

   Consider what 'every' means in this context.

4. 4.

   True or False: You need both AND and OR to create a functionally complete set.

   • True
   • False

   Hint

   Think about alternative sets of operators.

5. 5.

   Create a truth table to demonstrate the equivalence between p ∧ q and ¬(¬p ∨ ¬q).

   Hint

   Make sure to cover all possible truth values for p and q.

6. 6.

   Show that a set of logical operators including only NOT and NOR can still express all logical propositions.

   Hint

   Start by transforming implications first.