decompose to 3nf

Question

Answer 1

I think we can decompose to BCNF but it will violate the dependency preserving.
Here AC is the candidate key
BCNF decomposition 
R₁(ABC) (AC is the candidate key )        R₂(BCD) (BC⁺ is the candidate key)     R₃(DE) ( D⁺=DE D is the candidate key)

AC->BC                                                   BC->D                                               D->E
 

Further no decomposition is possible ! I guess. So option B
 

Comments

@arjun sir after directly applying bcnf decomposition algorithm for this question we will not get dependency preservation. but 3nf decomposition gives decompositions which are also in bcnf. so if we get bcnf decompositions from 3nf decomposition can we answer yes for such question?

---

No, In your decomposition, you get AC->D, FD and also A->B. And when you take closure, this covers BC->D. So, it is dependency preserving -- you might be applying the dependency check wrongly.

---

@vineet.ildm Sir , I am getting the same decomposition as yours.  So is it wrong? 

@Arjun Sir, please tell if it will dependancy preserving / not ?

because the 3NF form decomposition is also lossless.

Answer 2

Ans should be yes..!!

R1(A,B)

R2(A,C)

R3(B,C,D)

R4(D,E)

Answer 3

Answer is option b: NO

Cannot decompose into BCNF without violating Functional Dependency Preservation.