I tried to deal with this question: $$F(a,b,c,d) = (a'+b'+c')\oplus bcd$$ While I asked to prove that F with the constant '$0$' is universal gate.
I know that to prove that some function is universal gate so i need to simplify the function and show that the function is using NAND and NOR gates (that contains not, or, and).
Is thats what I need to prove here?
No. Take a look at the definition of universal set (of some gates and constants) again. It means that every propositional formula can be computed via a circuit that uses only gates and constants from such a set. So "i need to simplify the function and show that the function is using NAND and NOR gates" is false. The nand gate is universal already, so everything can be implemented using it alone, so proving that $F$ can be implemented using the nand gate says nothing at all about $F$.