# GATE 2004 50. The relation scheme Student Performance (name

GATE 2004
50. The relation scheme Student Performance (name, courseNo, rollNo, grade) has
the following functional dependencies:
name --->rollNo
rollNo  --->name
The highest normal form of this relation scheme is
(a) 2 NF (b) 3 NF (c) BCNF (d) 4 NF

• Explanation

Ans: B 3NF.

For simplicity , I will rename attributes as follows: name= N, course= C, grade= G, and rollnumber= R.

FDs are : NC->G, RC->G , N-> R, R->N.

PKs will be NC,RC. Prime attributes are { N,C,R} and non prime { G}

This relation is in 2NF as non prime attributes {G} is fully functionally dependent on PKs.

This relation is in 3NF as well because it is in 2NF and every FD is in either of the form X->Y,where

1) X is key( irrespective of Y)

OR

2) Y is prime attribute.

1st two FDs are of 1st kind and last 2 FDs are of second kind. So this relation is in 3NF.

It is not in BCNF, as BCNF specification says that each FD should be in form of X->Y where X should be a PK ( not primary attribute, but primary key ,composite or single valued.), which is not true in our relation in last 2 FDs.

So highest Normal Form of this relation is 3NF.

Let me know if I am unclear or wrong.