ISRO2020-50

Question

If every non-key attribute functionally dependent on the primary key, then the relation will be in

• A. First normal form
• B. Second normal form
• C. Third normal form
• D. Fourth Normal form

Comments

I will claim this question..

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Yes, it is not mentioned whether it is full or partial functional dependency.

The language of question is very poor as it can vary with different interpretations from $1-NF$, $2-NF$, and $3-NF$.

And if I don't presume anything then according to me $\mathbf{1-NF}$ is the only sure shot answer.

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R: {X→Y,  Y→Z,  X→Z}

In above relation,  in FD Y→Z, Z is clearly Non key attribute and It is NOT dependent on Primary key Because Primary key is X.  So, Y→Z is not correct FD for given statement. Answer has to be 3NF.

Answer 1

$\underline{\textbf{Answer:}\Rightarrow}\;\mathbf{b.}$

1 NF: atomic values

2 NF: Full Functional Dependency.

3 NF: No transitive dependency.

BCNF: Super Key

Edit: The language of this question is poorly framed as it is not mentioned whether we have a partial or full functional dependency.

So, answer can very according to the interpretations between $1-NF$ to $2-NF$.

Comments

@Debapaul 

in that answer the relation is in 3 NF not in 1NF. 

In that relation keys are AC and AB.

Since AC->B and C->B.

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R: {X→Y,  Y→Z,  X→Z}

In above relation,  in FD Y→Z, Z is clearly Non key attribute and It is NOT dependent on Primary key Because Primary key is X.  So, Y→Z is not correct FD for given statement. Answer has to be 3NF.

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a relation is in 3nf if either lhs of depenedency is a super key OR rhs is prime attribute.

for bcnf lhs should be super key for all dependencies of the realtion.

here clearly given that rhs is  key which is prime attribute.

I dont see why anyone would argue with this question

Answer 2

Answer : C) Third normal form.

2NF: All non-prime(non-key) attributes are dependent on the primary key.

3NF: All the non-prime(non-key) attributes must depend only on the candidate/primary key.

Comments

It will be 2nf man not 3nf

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Why it is not in 2NF:

Let's take simple example:

R: {X→Y,  Y→Z,  X→Z}

In above relation,  in FD Y→Z, Z is clearly Non key attribute and It is NOT dependent on Primary key Because Primary key is X.

Y→Z is not valid functional dependency for the given statement "If EVERY non-key attribute (like Z) functionally dependent on the primary key (Which is X)". 

Answer has to be 3NF

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Counter example taken is not correct, I think.

whenever there is Non-key in RHS, then there has to be a primary key in LHS.( for all Fd)

Y -> Z is not satisfied qsn statement, but X->Z satisfies qsn statement.

why all people are saying 2NF.

Answer 3

It has to be in 3NF as here we have X->Y where x is primary key which will have prime attribute and it will determine non prime attribute which is condition well held in 3NF

Answer 4

If every non-key attribute functionally dependent on the primary key, then the relation will be in

Let us take a relation R(A,B,C). 

Consider a functional dependency: AB -> C (this satisfies the statement). Let us add another fd to this relation. A -> C. Here we have a partial dependency. So it cannot be 2NF. So the relation has to be in 1NF only.

So Basically for relation

R(A, B, C)

 AB -> C

 A -> C

Had they given "If every non-key attribute functionally dependent only on the primary key, then the relation will be in..." then answer would have been 3NF. 

Also this was discussed long before here : https://gateoverflow.in/15778/every-attribute-functionally-dependent-primary-relation?show=323328#a323328

 

So answer is option A:1NF