f(A,B,C)=A'+BC' check functionally complete or not
If we are able to derive (AND,NOT) or (OR,NOT) then it is functionally complete otherwise not
For completement(Not) :
Do like this it is easy to find compliment
put f(A,A,A) orF(B,B,B) or f(C,C,C)
then we get completement, let we put f(A,A,A )in given function then we get
f(A,A,A)=A'.......(We got Completementi.e NOT)
Now try for 'OR' or 'AND'
Let check for 'OR' i.e f(A,B,C)=A+B
so put f( f(A,A,A),B,F(B,B,B)) in given function SO,
f( f(A,A,A),B,F(B,B,B) )=A+B.....( since we know f(A,A,A)=A' F(B,B,B)=B')
therefore we are able to get 'NOT' and 'OR' so this function is functionally complete
Note :If the given expression is not having any complement variable then it is not possible to get any complement(i.e NOT).Then directly we can say to that function is not functionally complete.
Example : f(A,B,C)=AB+BC+CA in this example we have no complemented variable then by looking directly to function we can say it is not functionally complete.