NIELIT 2018-58

Question

Consider the following functional dependencies in a database:

$A \rightarrow B$

$B \rightarrow C$

$D \rightarrow E$

$E \rightarrow D$

$F \rightarrow G$

$F \rightarrow H$

$(E,F) \rightarrow I$

The relation $(E,D,A,B)$ is

• A. $2$ NF
• B. $3$ NF
• C. BCNF
• D. None of the above

Comments

@Arjunsir what is the meaning of ( E,F ) -→ 1 ?? Is it typo ??

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Fixed now

Answer 1

If we observe FDs then AD & AE are candidate keys for this relation. 

Given relation is in 1NF because of PARTIAL DEPENDENCY like

$E\rightarrow D$ 

$D\rightarrow E$

therefore OPTION D.

 

Comments

D→ E and E->D are not partial dependencies … it is bcs of A->B which is a partial dependency .

Answer 2

For relation (A,B,D,E) FD are

A -> B

D -> E

E -> D

Candidate key is AD and AE. A -> B is partial dependency. Database by default is in 1 NF.

So D none of these is correct.

Answer 3

Functional dependencies of the given subrelation R(E,D,A,B) are:
A → B
D → E
E → D
Since A is not determined by any of the given functional dependencies for R(E,D,A,B) so it must be included in the key now check whether “A” is the Primary key or not.
(A)+ = {A}
(AB)+ = {AB}
(AD)+ = {ABDE}
(AE)+ = {ABDE}
So (AD)+ and (AE)+ are the primary keys of R(E,D,A,B).
A → B, in this given FD there exist a partial dependency because here a prime key attribute(attribute which is a part of primary key but not a primary key itself of a function) which is determining a non-key attribute.
So the relation R(E,D,A,B) is not in 2NF .