There are two functions
f(x,y,z) = x'yz + xy' + y'z'
g(x,y,z) = x'yz + x'yz' + xy
Are these functions functionally complete ?
For first one, We can have f(x,x,y) = (x + y)' which is NOR and is known to be functionally complete so f is functionally complete.
One small doubt I have here is, for proving NOR and NAND operations for 3 variables, do we have to include all 3 variables or is 2 variables enough ? Like is it enough if we check if f is capable of determining (x.y)' or should it be capable of determining (x.y.z)' and (x.y)' is not enough?
In second function I am not able to determine any of the known functionally complete sets like NAND or NOR. But I am not sure whether it is really not functionally complete.
Can someone help me with second function ?