Proving that a given gate is universal

Question

The question is:

Given gate called NEW has 4 inputs and 1 output

NEW(w,x,y,z)=zy(w+z)

Is NEW is Universal logic gate?

I found that the gate is not universal because I can't create NOT gate with it. How should I prove it? thanks

Answer 1

Show that $NEW(1,1,1,1)=1$, and then use induction to show that no matter $NEW$ gates you string together, you'll always end up with $1$ on the output if all inputs are $1$