If a relation is in Third Normal Form (3NF), which statement must hold?

Concept

For every non-trivial functional dependency X → A, Third Normal Form requires either X to be a superkey or A to be a prime attribute. Equivalently, a non-prime attribute cannot depend transitively on a key through another non-prime attribute.

Application

1. Take A as a non-prime dependent attribute. Then the branch that permits A to be prime is unavailable.

2. If X is another non-prime attribute, X cannot by itself be a superkey; therefore X → A violates the 3NF test.

Contrast

• A ban on every prime-to-non-prime dependency is too strong: a candidate key normally determines non-prime attributes.

• Functional independence of all attributes would eliminate the dependencies that define keys.

• 3NF constrains determinants of non-prime dependents; it does not state that prime attributes are independent of all non-prime attributes.

Cross-check

The formal dependency rule and IBM's normalization guidance both describe 3NF as avoiding dependencies of non-key attributes on other non-key attributes.

Result

Therefore, the required statement is: No non-prime attribute is functionally dependent on another non-prime attribute.