To obtain a NAND gate, you only need to add one NOT gate behind your AND gate.
To obtain a XOR gate you need to add again a NOT gate behind the XNOR gate. This circuit you can build no more, because the C-MOS IC 4001 provides only four NOR gates. But it certainly has become clear that you can actually build all the gates only with NOR gates.
With NAND gates you can also build all seven basic gates. But more on that later (Know more ...).
But enough for now of basic gates...