let's consider a table withcarID | hireDate | manufactory | model | custID | custName | outletNo | outletLocI want to evaluate all the functional dependencies to bring in first, second and then third normal form.Functional dependenciescarID,hireDate -> custIDPartial dependenciescarID->manufactory, model, outletNo**Transitive dependenciescustID->custNameoutletNo->outletLocSince a car is in a outlet only I have in the partial dependecies this:carID->manufactory, model, outletNo**However this leads to anomalies in insertion (imagine adding a car with no outlet), so should not that be like this?carID->manufactory, modelcarID->outletNoBut isn't this still an normalisation anomaly? 
Functional dependencies with the same key?
database theory;databases
I think you're misjudging what an insertion anomaly is. It does make sense for the FD to be carID -> manufactory, model, outletNo**since this is just a way to say that the same carID always has the same manufactory, model and outletNo.Now, if you leave aside for a moment custId and custName, and you decompose the relation this way:R1(carID, manufactory, model, outletNo), R2(outletNo, location)you see that this is a fine decomposition that meets 3NF and is free from insertion anomalies: infact you just cannot have, for example, the same carID in two distinct outlets, or the same outletNo with different location. You're right that adding a car with no outletNo would be no good since outletNo is a foreign key to R2, infact most DBs won't allow you to do such a thing. But this is a different story. Not providing values for mandatory fields is just wrong, and that of course doesn't mean the design of the database is not correct.