# GATE | GATE-CS-2004 | Question 90

The relation scheme Student Performance (name, courseNo, rollNo, grade) has the following functional dependencies:

```name, courseNo → grade
rollNo, courseNo → grade
name → rollNo
rollNo → name ```

The highest normal form of this relation scheme is
(A) 2 NF
(B) 3 NF
(C) BCNF
(D) 4NF

Explanation: For easy understanding let’s say attributes (name, courseNo, rollNo, grade) be (A,B,C,D). Then given FDs are as follows:

`AB->D, CB->D, A->C, C->A `

Here there are two Candidate keys, AB and CB.

Now AB->D and CB->D satisfy BCNF as LHS is superkey in both.

But, A->C and C->A, doesn’t satisfy BCNF. Hence we check for 3NF for these 2 FDs.

As C and A on RHS of both the FDs are prime attributes, they satisfy 3NF.

Hence for the whole relation the highest normal form is 3NF.

Quiz of this Question

My Personal Notes arrow_drop_up
Article Tags :

Be the First to upvote.

Please write to us at contribute@geeksforgeeks.org to report any issue with the above content.