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).
Because we have the candidate keys AB, BC and BD, 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. It follows that the relation scheme R must be in the third normal form!