Question

We have the attributes: {A, B, C, D, E, F, G}.

Consider the following functional dependencies

• F → C, D

• E → B

• B, D, G → C

• G → B, D

• B, G → D, E

• F → E

• B, E → A, F

• F, G → C, D

The minimal keys are:

• {G}

Determine whether these functional dependencies are in the following normal form(s): Third Normal form or Boyce Codd normal form

Answer 1

For simplicity assume that FD's are:-

F->CD

E->B

BDG->C

G->BD

BG->DE

F->E

BE->AF

FG->CD

candidate key = {G} (given)

Now,testing whether relation is in 3NF or not?

A relation is said to be in 3NF if all the functional dependencies of relation has its left side as super key or its right side as prime attributes(attributes which are part of candidate key)

Prime attributes here is G only.

Clearly, given relation has many FD's like F->CD, E->B,F->E and BE->AF which has neither its left side as super key or its right side as prime.

So,the given relation is not in 3NF.

A relation is said to be in BCNF if all the FD's in relation has its left side as super key.

Clearly, there are many FD's like F->CD,E->B,F->E and BE->AF which doesn't satisfy above requirements of BCNF.

So,the above relation is not in BCNF.

So,the given relation is neither in 3NF nor in BCNF.