Using NAND and NOR Gates
NAND Gates
You can make every logic gate by using only NAND gates:
Nor Gates
You can make every logic gate by using just NOR gates:
Overall Comparison
Look at he circuits above, two gates connected in the pattern above creates an AND gate with NAND and an OR gate with NOR.
Three gates connected in the pattern above will create an OR gate out of NAND and an AND gate out of NOR.
A single gate connected as above will create a not gate.