Dependency Preserving in decomposition of tables

Question

I am confused with dependency preserving property of database relations (tables). Do we have to look at initial FD set or what else? I tried to solve some problems on this subject. The questions before this one all feed my initial estimation, which is 'look at the given FD set. If you don't lose any of them in your new relation set, then this is dependency preserving'.

But when I come to this question I am confused.

Consider the relation R = (ABCDEFGH) and the following FD set:

• FD1 E -› D
• FD2 B, E -› CG
• FD3 D, G -› E
• FD4 C -› AB
• FD5 E, G -› C
• FD6 A, E -› BD
• FD7 C, E, D -› G
• FD8 A, G -› E

These are the given relations

• R1 (EFGH)
• R2 (ABEG)
• R3 (CDEG)
• R4 (ABC)

Answer says that this decomposition is dependency preserving. According to my estimation we lose FD2 so, this must not be dependency preserving.

I need an expert to clarify this concept for me.

Answer 1

This question was a part of homework questions. I wasn't sure if I am thinking right when I do the homework.

In my answer I wrote: This decomposition is not dependency preserving because in this decomposition we loose the FD DF--> BC .

And my database teacher accepted this answer as an right answer I wanted to clearify the subject here also.

Ferda

Answer 2

The decomposition is dependency preserving as FD2 BE->CG can be achieved by relations R2(BE->G) and R3(EG->C). Closure of BE gives CG.