Functionally complete

Question

F(x, y, z) =x + y'z' 

It's functionally complete according to normal procedure to implement NOT & OR or AND from it. 

But from this short trick.

https://www.google.co.in/amp/s/www.geeksforgeeks.org/gate-gate-cs-2015-set-1-question-49/amp

It's preserving 1.so it can't be functionally complete.

I must be wrong but I could not identify it. 

Comments

could you please tell me, how that function is functionally complete by normal procedure?

How you are able to derive NOT gate from the function, ( don't say it is partially functionally complete )

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So those rules (zero preserving, one preserving, linear, monotonic  self dual) are only for fully functionally complete functions; not for partially functional complete functions?

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yes

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Then this trick is no more useful as in gate they ask abt functionally complete(including fully & partially).

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A function is said to be functional complete if it derives $(-,\cdot ) or (+,\cdot )$.

for ex. f(x,y,z)=x+y'z' we can't gate not gate from the input variable x,y,z but we can get not gate by using 0    but it become partially complete not fully functionally complete.

Answer 1

NO ,you can't able to produce COMPLEMENT unless you will not give constant value (0 or 1) . So this function is not fully functionally complement but partially complete function.

This mistake may be you doing: f(x',y,y') = x' but this is not allowed. this means that you already have complement that is not the case. (passing x' is not allowed unless it already produced)