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Is this in BCNF?

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-1

Assume that the relation is obtained through decomposition from a relation with attributes ABCDEFGHI and that dependencies over ABCDEFGHI are listed below.

R(A,B,F)
B->E
A->F

We need to convert this relation into BCNF

What i have done till now is

R1(AB)
R2(AF)
R3(BE)

Is there anything more I should do? Is this proper BCNF or am I missing something?

database database-normalization functional-dependencies bcnf

share|improve this question

edited Apr 1 at 11:09

Mike Sherrill 'Cat Recall'

72k1313 gold badges9191 silver badges146146 bronze badges

asked Mar 27 at 10:57

sania00sania00

111 bronze badge

• 
  
  
  

  
  

  
  
  
  
  
  

  
  
  Re "is this right": Show the steps of your work following your reference/textbook, with justification--we want to check your work but not redo it & we need your choices when an algorithm allows them & otherwise we can't tell you where you went wrong (or right). See hits googling 'stackexchange homework.
  
  – philipxy
  Mar 27 at 20:42
  

  
  
  
  

add a comment | 

-1

Assume that the relation is obtained through decomposition from a relation with attributes ABCDEFGHI and that dependencies over ABCDEFGHI are listed below.

R(A,B,F)
B->E
A->F

We need to convert this relation into BCNF

What i have done till now is

R1(AB)
R2(AF)
R3(BE)

Is there anything more I should do? Is this proper BCNF or am I missing something?

database database-normalization functional-dependencies bcnf

share|improve this question

edited Apr 1 at 11:09

Mike Sherrill 'Cat Recall'

72k1313 gold badges9191 silver badges146146 bronze badges

asked Mar 27 at 10:57

sania00sania00

111 bronze badge

• 
  
  
  

  
  

  
  
  
  
  
  

  
  
  Re "is this right": Show the steps of your work following your reference/textbook, with justification--we want to check your work but not redo it & we need your choices when an algorithm allows them & otherwise we can't tell you where you went wrong (or right). See hits googling 'stackexchange homework.
  
  – philipxy
  Mar 27 at 20:42
  

  
  
  
  

add a comment | 

Assume that the relation is obtained through decomposition from a relation with attributes ABCDEFGHI and that dependencies over ABCDEFGHI are listed below.

R(A,B,F)
B->E
A->F

We need to convert this relation into BCNF

What i have done till now is

R1(AB)
R2(AF)
R3(BE)

Is there anything more I should do? Is this proper BCNF or am I missing something?

database database-normalization functional-dependencies bcnf

share|improve this question

edited Apr 1 at 11:09

Mike Sherrill 'Cat Recall'

72k1313 gold badges9191 silver badges146146 bronze badges

asked Mar 27 at 10:57

sania00sania00

111 bronze badge

share|improve this question

edited Apr 1 at 11:09

Mike Sherrill 'Cat Recall'

72k1313 gold badges9191 silver badges146146 bronze badges

asked Mar 27 at 10:57

sania00sania00

111 bronze badge

share|improve this question

edited Apr 1 at 11:09

Mike Sherrill 'Cat Recall'

72k1313 gold badges9191 silver badges146146 bronze badges

asked Mar 27 at 10:57

sania00sania00

111 bronze badge

edited Apr 1 at 11:09

Mike Sherrill 'Cat Recall'

72k1313 gold badges9191 silver badges146146 bronze badges

edited Apr 1 at 11:09

Mike Sherrill 'Cat Recall'

72k1313 gold badges9191 silver badges146146 bronze badges

asked Mar 27 at 10:57

sania00sania00

111 bronze badge

asked Mar 27 at 10:57

sania00sania00

111 bronze badge

1 Answer
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This answer follows from the edited question, under the following hypotheses:

1. the original relation is R(ABCDEFGHI)


2. a cover of the functional dependencies holding on it is B->E, A->F
   

Of course if my hypotheses are wrong the answer is wrong!

In this case:

1. the only candidate key of the original relation is ABCDGHI;


2. in the decomposed relation R1(ABF) the only non-trivial dependency that holds is A -> F, so the relation has the only candidate key AB;


3. the relation is not in BCNF, and a decomposition in BCNF is R2(AF), R3(AB)
   

Note that you cannot decompose a relation adding an extraneous attribute, like E in your decomposition.

share|improve this answer

edited Mar 28 at 10:44

answered Mar 27 at 11:34

RenzoRenzo

19.1k44 gold badges3535 silver badges4848 bronze badges

• 
  
  
  

  
  

  
  
  
  
  
  

  
  
  Thank you for your input sir.But i'm a bit confused about it not being BCNF. Is there an algorithm I could follow to convert it to bcnf?
  
  – sania00
  Mar 27 at 11:59
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  
  There are algorithm described more or less formally in books on databases. A sketch of an algorithm is shown here.
  
  – Renzo
  Mar 27 at 14:34
  

  
  
  
  

add a comment | 

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0

This answer follows from the edited question, under the following hypotheses:

1. the original relation is R(ABCDEFGHI)


2. a cover of the functional dependencies holding on it is B->E, A->F
   

Of course if my hypotheses are wrong the answer is wrong!

In this case:

1. the only candidate key of the original relation is ABCDGHI;


2. in the decomposed relation R1(ABF) the only non-trivial dependency that holds is A -> F, so the relation has the only candidate key AB;


3. the relation is not in BCNF, and a decomposition in BCNF is R2(AF), R3(AB)
   

Note that you cannot decompose a relation adding an extraneous attribute, like E in your decomposition.

share|improve this answer

edited Mar 28 at 10:44

answered Mar 27 at 11:34

RenzoRenzo

19.1k44 gold badges3535 silver badges4848 bronze badges

• 
  
  
  

  
  

  
  
  
  
  
  

  
  
  Thank you for your input sir.But i'm a bit confused about it not being BCNF. Is there an algorithm I could follow to convert it to bcnf?
  
  – sania00
  Mar 27 at 11:59
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  
  There are algorithm described more or less formally in books on databases. A sketch of an algorithm is shown here.
  
  – Renzo
  Mar 27 at 14:34
  

  
  
  
  

add a comment | 

0

This answer follows from the edited question, under the following hypotheses:

1. the original relation is R(ABCDEFGHI)


2. a cover of the functional dependencies holding on it is B->E, A->F
   

Of course if my hypotheses are wrong the answer is wrong!

In this case:

1. the only candidate key of the original relation is ABCDGHI;


2. in the decomposed relation R1(ABF) the only non-trivial dependency that holds is A -> F, so the relation has the only candidate key AB;


3. the relation is not in BCNF, and a decomposition in BCNF is R2(AF), R3(AB)
   

Note that you cannot decompose a relation adding an extraneous attribute, like E in your decomposition.

share|improve this answer

edited Mar 28 at 10:44

answered Mar 27 at 11:34

RenzoRenzo

19.1k44 gold badges3535 silver badges4848 bronze badges

• 
  
  
  

  
  

  
  
  
  
  
  

  
  
  Thank you for your input sir.But i'm a bit confused about it not being BCNF. Is there an algorithm I could follow to convert it to bcnf?
  
  – sania00
  Mar 27 at 11:59
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  
  There are algorithm described more or less formally in books on databases. A sketch of an algorithm is shown here.
  
  – Renzo
  Mar 27 at 14:34
  

  
  
  
  

add a comment | 

This answer follows from the edited question, under the following hypotheses:

1. the original relation is R(ABCDEFGHI)


2. a cover of the functional dependencies holding on it is B->E, A->F
   

Of course if my hypotheses are wrong the answer is wrong!

In this case:

1. the only candidate key of the original relation is ABCDGHI;


2. in the decomposed relation R1(ABF) the only non-trivial dependency that holds is A -> F, so the relation has the only candidate key AB;


3. the relation is not in BCNF, and a decomposition in BCNF is R2(AF), R3(AB)
   

Note that you cannot decompose a relation adding an extraneous attribute, like E in your decomposition.

share|improve this answer

edited Mar 28 at 10:44

answered Mar 27 at 11:34

RenzoRenzo

19.1k44 gold badges3535 silver badges4848 bronze badges

share|improve this answer

edited Mar 28 at 10:44

answered Mar 27 at 11:34

RenzoRenzo

19.1k44 gold badges3535 silver badges4848 bronze badges

answered Mar 27 at 11:34

RenzoRenzo

19.1k44 gold badges3535 silver badges4848 bronze badges

answered Mar 27 at 11:34

RenzoRenzo

19.1k44 gold badges3535 silver badges4848 bronze badges