What is the highest Normal Form of the following table ?

Each Owner has only one Pet with one PetColour and PetAge.

Each Pet has only one Vet.

Question

What is the highest Normal Form of the following table ?

Each Owner has only one Pet with one PetColour and PetAge.

Each Pet has only one Vet.

BlackTom AI · Accepted Answer

We start by restating the scenario: the table has attributes Owner, Pet, PetColour, PetAge, Vet, and the givens say each Owner has exactly one Pet (with one PetColour and PetAge) and each Pet has exactly one Vet.

Option 1: 2NF
- To be in 2NF, the table must be in 1NF and every non-prime attribute must be fully functionally dependent on every candidate key (no partial dependency of a non-prime attribute on a part of a candidate key).
- Here, the only candidate key is Owner, since Owner determines the Pet, PetColour, PetAge, and Vet via the chain Owner -> Pet and Pet -> (PetColour, PetAge, Vet).
- There are no partial dependencies on a part of a composite key because the key is a single attribute (Owner). Thus, there are no violations of 2NF from partial dependencies.
- However, we need to check for transitive dependencies which are not prohibited by 2NF; those are allowed in 2NF but would affect higher normal forms.

Option 2: None of the answers
- If 2NF is the correct form, claiming none of the answers would be wrong, since there is a valid NF that applies here given the stated dependencies.

Option 3: BCNF
- In BCNF, every non-trivial FD X -> A must have X as a superkey.
- We have Owner -> Pet, PetColour, PetAge, Vet. The left side Owner is a superkey, so that FD is fine.
- But there is also the dependency Pet -> Vet, PetColour, PetAge. The left side Pet is not a superkey (Owner is the only candidate key), so this FD violates BCNF.
- Therefore the relation cannot be in BCNF.

Option 4: 1NF
- 1NF simply means the relation has atomic attribute values; this is the base requirement for relational tables.
- Given the data structure and dependencies, the relation can be assumed to be in 1NF, but since we can achieve at least 2NF as discussed, 1NF is not the highest normal form here.

Summary of reasoning across options:
- The chain Owner -> Pet -> (Vet, PetColour, PetAge) shows that Owner is a key, while Pet determines other attributes but is not a key on its own. This implies a transitive dependency from Owner to Vet via Pet, which prevents BCNF.
- Because there are no partial dependencies on a composite key (the key is not composite), 2NF is satisfied as a valid higher form relative to 1NF, but the presence of a transitive dependency means we do not reach 3NF or BCNF.
- 1NF is satisfied, but not the highest form given the transitive dependencies; 2NF remains the highest normal form that holds for this design.

Note: The critical observations are the existence of a non-key determinant (Pet) determining another non-prime attribute (Vet, plus PetColour and PetAge), which breaks BCNF and 3NF conditions, while 2NF remains acceptable because the only candidate key is a single attribute (no partial dependency on a part of a composite key).

What is the highest Normal Form of the following table ? Each Owner has only one Pet with one PetColour and PetAge. Each Pet has only one Vet.

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