Translating functional dependencies into 3rd normal form

Question

I have this problem decomposing a relation schema into a set of schemas that are in 3NF.

I have this relation schema: R= (A, B, C, D, E, F)
With the following set F of functional dependencies:

A → ABCDEF
B → C
D → E

Can anyone help me out?

Answer 1

R_A = (A, B, D, F)
R_B = (B, C)
R_D = (D, E)

Why? 3NF requires the removal all non-transitive dependencies.

In R, C is transitively dependent on A through B, and the same is true for E through D. To remove those properties, you need to decompose the tables such that those transitive relationships are removed, which you do by extracting the table and using the middle term as keys.