I need help with logic sim, i need to construct a NOR or XOR circuit using NAND gates only.

I have created one already, just wanted to make sure it was correct, I have input 1 and input 2, going into a NOR gate and then output 3.

Is this correct? Or do I need to add a NAND gate in there somewhere..

Also i need to construct a truth tabele for boolean function,

M = x *(y * inverted Z + inverted x * y)

Then I need to build a circuit in logic sim for this..

Can anybody help with these two questions,

thanks