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UGC NET Computer Science Nov 2021 (Paper II)

Given a relation scheme $R(x,y,z,w)$ with functional dependencies set

$F=\{x\to y,\ z\to w\}$.

All attributes take single and atomic values only.
A. Relation $R$ is in First Normal Form
B. Relation $R$ is in Second Normal Form
C. Primary key of $R$ is $xz$
Choose the correct answer from the options given below:

Solution

All attributes are single and atomic.

So, relation $R$ is in $1NF$.

Hence, statement A is true.

Now find key:

$x\to y$ and $z\to w$

So,

$(xz)^+=\{x,z,y,w\}$

Thus, $xz$ is a candidate key.

Hence, statement C is true.

For $2NF$, no non-prime attribute should depend on a proper part of candidate key.

But here,

$x\to y$

and

$z\to w$

Here $y$ and $w$ are non-prime attributes, and they depend on parts of key $xz$.

So, partial dependency exists.

Therefore, $R$ is not in $2NF$.

Hence, statement B is false.

Therefore, A and C only are correct.

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