Question

I am trying to comprehend BCNF databasing and I can’t quite wrap my head around it.

Consider the following relation:

R (A, B, C, D, E, F, G)

The following functional dependences hold:

A -> E, F
A -> G
A, B -> D
B -> C
E, F -> G
A -> D

How would I make it BCNF?

Answer 1

Speaking informally, in homework problems, you get to BCNF by

• assuming you’re in at least 1NF,
• removing partial key dependencies to get to 2NF (at least),
• removing transitive dependencies to get to 3NF (at least), and finally
• removing remaining functional dependencies in which the left-hand side isn’t a candidate key to get to BCNF (at least).

An example of a partial key dependency is the pair

AB->D
A->D

Since A alone determines D, the functional dependency AB->D has a partial key dependency.

An example of a transitive dependency is the pair

A->EF
EF->G

There’s no guarantee that you can normalize a given relation to, say, BCNF and no higher. (This seems to cause a lot of confusion among university students on SO.) Removing partial-key dependencies to get to 2NF might leave all the relations in 5NF.