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Consider the relational  schema S= {A,B,C,D} and the following functional dependencies on S:

$A$$\rightarrow BCD$
$B$$\rightarrow C$
$CD$$\rightarrow A$

Which of the following is true?

  1. $S$ is in $3NF$ and also in $BCNF$
  2. $S$ is in $2NF$ not in $3NF$
  3. $S$ is in $3NF$ but not in $BCNF$
  4. $S$ is in $BCNF$ but not in $4NF$
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Candidate keys: A, CD, BD.         

     Prime attributes: A, B, C, D,

   here  B -> C violates  BCNF  condition
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Answer : c

C.K = {A},{CD},{BD}

it's in 1NF :-

it's in 2NF :- every non-prime attribute is fully functionally dependent on each C.K . there is no non-prime attribute on RHS , so it's in 2NF

 

it's in 3NF :- no non-prime attribute is functionally dependent on non-prime attribute , there is no non-prime attribute on RHS , so, it's in 3NF .

 

it's not in BCNF :- for BCNF , 3NF must be hold , and another condition is that if a->b then a must be superkey , but in B->C , B is not superkey , it's just prime attribute , (A→BCD , CD→A holds  BCNF property) . 

Answer:

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