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
- A.
in first normal form but not in second normal form
- B.
in second normal form but not in first normal form
- C.
in third normal form
- D.
None of the above
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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.