DB Functional Dependencies.

Question

I understand the concept of functional dependencies in Databases, but when it comes down to a format like this, I can't seem to wrap my head around it.

**Relation:**
A  B  C
a1|b1|c1
a2|b1|c1          
a1|b2|c2
a1|b1|c2
a3|b2|c1
a2|b1|c2    

Which functional dependencies exist in this relation?

Answer 1

Functional dependencies hold in/apply to a database DESIGN.

They do not "exist in a relation". It could be said of a relation that it SATISFIES some [set of] functional dependencies, but it is meaningless and confused to say that a functional dependency "exists in a relation".

As Victor more or less pointed out, your example relation satisfies only the trivial FD {ABC} -> {ABC}.

As for your other question, "what normal form is this relation in", once again this question is completely meaningless and confused, because the property of "being in some normal form", applies only to a design, not to some particular relation value. In relational terms : only a relation variable can be in some normal form, depending on which FDs are suppposed to hold in it, but a relation value cannot have such a property.

So, assuming that you are indeed talking of [the declaration of] a relation variable with a heading {A B C}, in which there are no nontrivial FDs (i.e. only {ABC} -> {ABC} holds), this relation variable is at least in BC normal form.

If there are no join dependencies, then your relvar is also in sixth normal form (no that's not a counting error).

Answer 2

There are none.

A functional dependency implies that, after eliminating any duplicates involving both the dependent and determinant columns, you can stick an UNIQUE onto the determinant columns. For instance, UNIQUE(A,B) does not work because a1,b1 appears twice, UNIQUE(A,C) fails because a1,c2 appears twice, and UNIQUE(B,C) fails because b1,c1 appears twice.