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


Answer: (B)

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.

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