The operations AND, OR, and NOT are universal in that any Boolean function can be implemented using just these three gates.
a. Prove by construction that the NAND gate is universal by creating AND, OR, and NOT gates using only the NAND gate.
b. Prove by construction that the NOR gate is also universal.
c. Why are the AND and OR gate not universal? (e.g. what simple operation cannot be created with just an AND or OR gate?)