7.2. Question 8

Try these first

1. 1.

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

   Hint

   Think about what it means to represent all expressions.

2. 2.

   Can you list the three main logical operators discussed in this section?

   Hint

   Consider the basic building blocks of logical expressions.

3. 3.

   Which of the following sets of operators is functionally complete?

   • {AND
   • OR
   • NOT}
   • {AND
   • OR}
   • {NOT}

   Hint

   Think about the definitions you've learned.

4. 4.

   True or False: You can represent every logical proposition using only disjunction and negation.

   Hint

   Recall the completeness established in your studies.

5. 5.

   Show that the set {Negation, AND} is functionally complete by deriving an expression for 'p or q'.

   Hint

   Use De Morgan's laws to guide your rewriting.

6. 6.

   If only NAND operators are available, can you represent the operation 'p and q'? Show your steps.

   Hint

   Think about how NAND relates to other operations.