How should the relation be decomposed so that it is in BCNF ?

Question

In the relation R(ABCD) , AB-->C , C-->AD 
How should the table be decomposed so that it is in BCNF , One decomposed relation will be ACD ,what should be other should it be BC , but if it is then there is no functional dependency corresponding to it and if I do ABC , then I have C-->A but C is not a superkey in ABC , so how should the decomposition be done ?

Comments

May be R1(A B C) , R2(C,D)

Answer 1

Here , in this example , BCNF & Dependency preservation is not simultaneously possible.

This type of problem occurs when we have AB -> C , C -> A type of Dependency.

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R1 (A C D)   , R2 (B C)  - If we decompose like this we are having BCNF , but AB -> C dependency is lost.

Answer 2

R(ABCD)

AB-->C C-AD

we can see candidate key here is{AB,BC}

For BCNF the FD Set:

X-->Y

where x should be super key

but we can see that C-->AD failed to satisfy bcnf.

Decompose into

R1(ABC)      R2(CD)    R3(AC)

AB-->C.         C-->D.      C-->A

Key{AB}       Key{C}     Key{C}

Minimum 3 table required ,2 Foreign key required.

BCNF not satisfied ,dp decomposition satisfied. If you want to satisfy BCNF You will definitely loose dp decomposition.

Comments

Lossless & BCNF is possible.

Dependency Preserving & BCNF is not possible.

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But the given decomposition is not lossless.

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check my answer.

Answer 3

R(ABCD) AB-->C C-AD Decompose into R1(ABC) R2(ACD)