Which of the normal form does the given relation satisfy

Find the normal form of the given relation schema / Which of the normal form does the given relation satisfy? / The relational table is in 2NF, 3NF or BCNF?

Question:

4. Assume a relation R with the schema R(A, B, C, D, E) and a set F of functional dependencies as follows; F = {A → B, C → D, D → E} The relation R is not in Second Normal Form (2NF). Why?

(a) R has no repeating groups
(b) R has transitive functional dependencies
(c) R has partial functional dependencies
(d) R has no key

Answer:

(c) R has partial functional dependencies

As per the question,

• Given - Schema of relation R and the set F of functional dependencies.

• Not known - The key.

The key for R is AC, a composite key (combination of two or more attributes). When we have composite keys, we need to verify that all the non-key attributes are fully functionally dependent on the whole key or not. In our question, the non-key attributes are B, D, and E. B is fully functionally dependent on A alone (A is part of AC, and B is partially dependent on AC), D is fully functionally dependent on C alone (C is part of AC, and D is partially dependent on AC). Hence, the rule for 2NF is violated and R is not in 2NF.

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