7.2.1. Functionally Complete Set of Logical Operators

Try these first

1. 1.

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

   Hint

   Think about the ability to represent all logical statements.

2. 2.

   How does the implication operator relate to disjunction?

   Hint

   Recall the transformations we've discussed.

3. 3.

   What is a functionally complete set of operators?

   • A set that can express all possible statements
   • A set that can only express simple statements
   • A set of random logical operators

   Hint

   Think about all logical statements that can be generated.

4. 4.

   True or False: Negation alone is enough to express all logical propositions.

   • True
   • False

   Hint

   Consider what other operators are needed.

5. 5.

   Prove that a set consisting of only disjunction and negation can be functionally complete.

   Hint

   Use De Morgan's laws and equivalency transformations.

6. 6.

   Create a combination of logical operators that demonstrates the transformation from biconditional to only conjunction and negation.

   Hint

   Start with what defines biconditional in terms of its implications.