## Newbie question about relvar normalization

Hi all,

first of all I have no clear idea on where to post this question It's about normalizing relvars.

I read C.J. Date's books SQL and Relational Theory (2009) and Database Design and Relational Theory (2012) (and loved them both). I believe that the author is respected in his field and I believe that the definitions he gives are accurate. I have a newbie question about normalizing relational variables up to 2. normal form.

First, some definitions on which I base my actual question so that we are on the same page.

Date defines the 1NF like this (Date, 2012):

Definition [of 1NF]: Let relation r have attributes A1, ..., An, of types T1, ..., Tn, respectively. Then r is in first
normal form (1NF) if and only if, for all tuples t appearing in r, the value of attribute Ai in t is of type Ti
(i = 1, ..., n).
And the 2NF like this (same source):

Definition [of 2NF]: Relvar R is in second normal form (2NF) if and only if, for every nontrivial FD X --> Y that
holds in R, at least one of the following is true: (a) X is a superkey; (b) Y is a subkey; (c) X is not a subkey.
Actually he gives another definition first, but says that the above is "logically equivalent" that definition, however has the same problem I'm about present. I have also heard other definitions of the 2NF, which actually answer the problem I introduce below. But I want to focus on this definition above, more so that it is accepted by C.J. Date himself.

Now the actual question(s): suppose we have relation variable R with attributes A, B and C and that a functional dependency {A} --> B holds (and no other).

a) is the relation R a relation at all? Why (not)?
b) is the relation R in 1NF? Why (not)?
c) is the relation R in 2NF? Why (not)?

The main question is why is it not in 2NF? The definitions above do not answer this question, because for FD {A} --> B the section a) in the 2NF's definition is TRUE. And there are no other non-trivial FDs in R. So according to those definitions, relation R is in second normal form (in which it clearly is not). I have been thinking this for several days and the only cause of the problem I have been able to conjure up is that I do not really understand what a relation is. I tried looking a definition up in Codd's paper (1970) but with no luck.

I hope the question is clear, English is not my main language. I hope that your answers address the questions based on the NF definitions above! I'm waiting for a good conversation