Normalization

Question

consider a relation R(ABCDE) with FD's={A->BC, CD->E, B->D,E->A}.

How many minimum relations require to decompose into BCNF with dependency preservation and lossless join decomposition?

Comments

4 RELATIONS?

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https://gateoverflow.in/63156/normalize-upto-bcnf

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I am getting 3 but dependency is lost.can we preserve dependency in this case after decomposing into 3 relations?

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^What are those?

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CDE, BD,ABCE

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ABCE won't be in BCNF. E is the key there.

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CDE,BD,ABC, AE? Would it be correct?

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Yes, that is always correct. Only question is if that can be minimized.

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i think it can't be minimized further

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Sorry, actually $E\to A, A\to E$.So, both $E$ and $A$ are candidate keys in $ABCE$. So, 3 should be the answer as you told first.

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yes! that's where i was confused :p Thanks anyway!

Answer 1

B-->D violeting the bcnf so make

R1= {B,D}

R2={A,B,C,E}

but here CD-->E is lost..

R2={A,B,C,E}

R3={C,D,E}

So I think 3 relations are needed...

Comments

R(ABCE)

A->BC,E->A

here key is{E} but BCNF DECOMPOSITION IS NOT POSSIBLE .

Answer 2

Dependency preservation can not possible although we can decompose in BCNF & lossless join but when we try to preserve dependency relation will not be BCNF