Consider the operations defined as f(X, Y, Z) = X'YZ + XY' + Y'Z' and g(X′, Y, Z) = X′YZ + X′YZ′ + XY .

Iam following this method,

A function is said to be complete if it can implement Complementation and OR logic / Complementation and AND logic.

For function f(X,Y,Z) = X'YZ + XY' + Y'Z'

f(X,X,X) = X'XX + XX' + X'X' = X' ( Complement logic)

Now if i can implement either OR / AND logic , then can i say function is complete??

But for g(X′, Y, Z) = X′YZ + X′YZ′ + XY

g(X',X',X') = XX'X' + XX'X' + X'X' = X' (Expected ans is X as X is complement of X', hence this is functionally incomplete).

How to prove OR / AND logic is possible for f(X,Y,Z)?