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The relation scheme $\text{Student Performance (name, courseNo, rollNo, grade)}$ has the following functional dependencies:

  • name, courseNo, $\rightarrow$ grade
  • rollNo, courseNo $\rightarrow$ grade
  • name $\rightarrow$ rollNo
  • rollNo $\rightarrow$ name

The highest normal form of this relation scheme is

  1. $\text{2NF}$
  2. $\text{3NF}$
  3. $\text{BCNF}$
  4. $\text{4NF}$
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Answer – B

We’ll first find all the candidate keys of given relation – 

  1. Closure of { name, courseNo } = { name, courseNo, rollNo, grade }
  2. Closure of { rollNo, courseNo } = { name, courseNo, rollNo, grade }

We’ve 2 candidate keys { name, courseNo } and { rollNo, courseNo }.

Therefore, prime attributes are { name, rollNo, courseNo }.

A relation is in 2NF if it is in 1NF and it has no partial dependency ie for all non-trivial FD X → Y, if Y is non-prime attribute then X must not be a proper subset of any candidate key. Here, we’ve no partial dependency. Thus, relation is in 2NF.

A relation is in 3NF if it is in 2NF and it has no transitive dependency ie for all non-trivial FD X → Y, either X is a super key or Y is a prime attribute. Here, we’ve no transitive dependency. Thus, relation is in 3NF.

A relation is in BCNF if it is in 3NF and for all non-trivial FD X → Y, either X is a super key. Here, name → rollNo and name is not a super key. Thus, relation is not in BCNF.

If a relation is not in BCNF, then it cannot be in 4NF.

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