ISRO CSE 2014 | Question: 63

Question

Consider the following table

The table is in which normal form?

• A. First Normal Form
• B. Second Normal Form
• C. Third Normal Form but not BCNF
• D. Third Normal Form and BCNF

Comments

Underline is used to indicate Primary Key, Not candidate key.

Here, by underline, it means that $AB$ is a primary key. There can be more candidate keys.

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A,B and C are prime attributes as AB and AC both are ck so C->B doesn't violet 3nf

Answer 1

Answer : C

Third Normal Form but not BCNF

See the dependencies 

AB ---> CDE

C ---> B

C is not a Super key Here

Comments

can B be considered as a prime attibute?

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yes B is prime attribute along with A and C

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Sorry but C is not a prime attribute. Prime attributes are those which are part of candidate key.

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@Gaurav , here AB and AC are candidate keys .. So A,B and C are prime attributes..

Answer 2

Answer : C

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Dependency: 

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AB ---> CDE

C ---> B

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1NF(yes): assume all attributes are atomic

2NF(yes): no partial functional  dependency like A alone can derive C or D or E

3NF(yes): no transitive functional dependency or there is nothing like (non key)-->(non key)

BCNF(no): in non trivial FD C-->B  , C is not a SuperKey.

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Answer 3

AB is the key here which determines C ,D E there is no P.D  and T.D between C,D,E SO IT IS IN 3NF

Now for BCNF every determinant is a candidate key determinant here are A,B,C (as C determines B) but C is not  candidate key hence it is not in BCNF (only if C->B is removed it becomes BCNF)

AC is also key  which can determine B and so also  D , E  but B is not candidate key

hence ans is C

Comments

AC is also a key

Answer 4

It is 3NF 

Bcz AB->CDE ,here we can clealy see that AB is super keys that's why it will be in 3NF and BCNF but C->B it is in 3NF not in BCNF that's why we can say that it will be in 3NF not in BCNF bcz both of them should be in BCNF not single one.

Answer 5

Correct Option is (C)
FD = { AB-->C , AB-->D, AB-->E, C-->B }
CK : AB and AC

• BCNF : Not in BCNF since C is not a SK in C-->B.
• 3NF : It's in 3NF since there's no CK that can transitively determine any Non-Prime attribute