For a database relation R(a,b,c,d), where the domains a, b, c, d include only…

1997

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

{ a → c, b → d } 

This relation is

  1. A.

    in first normal form but not in second normal form

  2. B.

    in second normal form but not in first normal form

  3. C.

    in third normal form

  4. D.

    None of the above

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Show answer & explanation

Correct answer: A

Since all domains contain only atomic values, R is in first normal form (1NF).

From the dependencies a → c and b → d, neither a nor b alone determines all attributes of R. Together, {a, b} determines a, b, c, and d, so {a, b} is a candidate key.

The non-prime attribute c depends only on a, and the non-prime attribute d depends only on b. These are partial dependencies on parts of the composite key {a, b}. Therefore, R violates second normal form (2NF).

Hence, the relation is in first normal form but not in second normal form.

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