Question 55

From Question 54, the candidate keys of $R$ are:

1. Prime and non-prime attributes:

   • Prime attributes (attributes participating in at least one candidate key): $\{A, B, D, E, F\}$.
   • Non-prime attributes: $\{C, G, H\}$.

2. Check for Second Normal Form (2NF):
   A relation is in 2NF if and only if every non-prime attribute is fully functionally dependent on every candidate key (i.e., no non-prime attribute depends on a proper subset of any candidate key).

   • Consider the candidate key $AD$ and the functional dependency $A \rightarrow BC$.
   • Attribute $C$ is a non-prime attribute, and it is functionally determined by $A$, which is a proper subset of the candidate key $AD$.
   • Similarly, in $B \rightarrow CFH$, non-prime attributes $C$ and $H$ depend on $B$, a proper subset of candidate key $BD$.
   • These partial dependencies violate 2NF.

3. Conclusion:
   Since the fields contain atomic values, $R$ is in 1NF, but fails 2NF due to partial dependencies of non-prime attributes on parts of candidate keys.

Therefore, $R$ is in 1NF, but not in 2NF, which is option (A).