7.2.2. Proving Functionality with Three Operators

Try these first

1. 1.

   What does it mean for a set of operators to be functionally complete?

   Hint

   Think about what types of statements can be created.

2. 2.

   Rewrite the implication p → q using conjunction and negation.

   Hint

   Remember how we can break down implications.

3. 3.

   What is the definition of a functionally complete set?

   • A set that cannot express all propositions
   • A set that can express all possible propositions
   • A set of three operators only

   Hint

   Think about the utility of the operators.

4. 4.

   Is the statement p → q equivalent to ¬p ∨ q?

   • True
   • False

   Hint

   Relate this to the definitions you've learned.

5. 5.

   Using only the operators AND and NOT, prove how you can express the complex proposition p || (q && r).

   Hint

   No hint provided

6. 6.

   Show that a biconditional can be transformed into disjunctions and negations and then back into its original form, demonstrating the reversibility of logical identities.

   Hint

   No hint provided