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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.
You can use our Flash circuit maker to build your circuits if you wish to see them in action, although this obviously does not prove your results.