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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

Felix
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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 $1$

Bram28
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  • Thanks! is it possible to prove also by truth table? – Felix Aug 09 '19 at 16:41
  • You need a meta-logical argument .. so you could reason about truth-tables, but you can't prove this using a single truth-table. – Bram28 Aug 10 '19 at 10:05