Not another NAND!

Prove that you can make any type of logic gate using just NAND gates.

Problem



 


The NAND gate is said to be universal. This means that the effect of any other logic gate can be replicated using just NAND gates.

Prove that this is indeed the case: replicate AND, OR, XOR, XNOR, NOR, NOT gates using just NAND gates.

Are any of the other types of gate universal? Prove it.