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For a database relation R(a, b, c, d) where the domains of a, b, c and d include only atomic values, only the following functional dependencies and those that can be inferred from them hold a → c b → d The relation is in

For a database relation R(a, b, c, d) where the domains of a, b, c and d include only atomic values, only the following functional dependencies and those that can be inferred from them hold a → c b → d The relation is in Correct Answer First normal form but not in second normal form

Concept:

2NF: There should not be any partial dependency in the relation.

3NF: There should not be any transitive dependency and right side of functional dependency is a prime attribute

BCNF: Left side of functional dependency is a key

If a functional dependency is in BCNF, then it will also be in lower normal forms (1 NF, 2NF, 3 NF). Also, if anyone functional dependency is in the weaker normal form, then the relation will be in weaker normal form

Explanation:

Functional dependencies are:

a → c

b → d

Candidate key for the relation R is  {ab}

Because (ab)+ = {a, b, c, d}

1) a → c

This is not in BCNF, because left side is not the candidate key. Also, not in 3NF because right side is not the prime attribute. It is in not in 2NF, because there exists partial dependency in this functional dependency, as a non-prime attribute is dependent on prime attribute. It is in 1NF.

2) b → d

Similar case as that of 1st functional dependency. It is in 1NF

So, given relation R (a, b, c, d) is in 1NF.

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