Suppose we have a relation R(A, B, C, D). If R has the following functional dependencies:
A, C -> D
B, C -> D
A -> B
B -> A
We should have the following candidate keys:
{A, C}, {B, C}
Thus, A, B and C are prime attributes.
I chose {A, C} as the primary key.
At this point I have arrived at an impasse.
While, from my experience, when normalising to the 2nd Normal Form it would be advisable to split the relation into:
R1(A, C, D)
R2(A, B)
But technically, following the requisites of the 2nd Normal Form, this isn't necessary as R is already in 2nd Normal Form.
Should I follow my gut and separate the relation or should I leave it as it is?