# In which normal form is the relation R?

Hello Community,

To prepare for my exam I have completed many exercises. Most of them were solvable without any problems. But the following task I could not solve until now. It is:

You are given the relation scheme `R (A,B,C,D)` with the three functional dependencies:

• `AB → C`
• `C → D`
• `D → A`

In which normal form is `R` (1st, 2nd or 3rd)? Justify your statement.

Could anyone of you please help me? A good explanation and substantiation would be very, very good!

Thank you sooo much!

P.S.: I already have one solution from a friend. But I do not know if it is correct…

He said that it is the second normal form because the non-key attributes `C` and `D` are fully functional depending on `A, B`. Besides he mentioned that it is not the third normal form because there is a transitive dependence between the non-key attributes (`A, B → C` and `C → D`).

• You should first try to find all candidate keys (hint: it's not only `AB`, there are others). Then, you'l lbe able to proceed. Jan 8, 2018 at 11:42
• Ok! I think the candidate keys are AB and BC. So yes it results in the second normal form, right? Jan 8, 2018 at 12:15
• What about `BD`? Jan 8, 2018 at 12:15
• BD? Ok... actually yes?! Now we have AB, BC and BD. So we have no non-key attributes. This means that the second normal form is approved, because no non-key attribute partially depends on a key. So the relation scheme R must be in the third normal form? Jan 8, 2018 at 12:44
• Yes, that is correct! You may post an answer ;) It is in 3NF (but not in BCNF) Jan 8, 2018 at 12:49