Functional dependencies: If attributes A and B together determine attribute C (written (A, B) → C), what else is necessarily true?

Introduction / Context:
Functional dependencies (FDs) express how attributes relate. Understanding what can and cannot be inferred from a given FD is central to normalization (e.g., 2NF, 3NF, BCNF).

Given Data / Assumptions:

• We are given (A, B) → C.
• No other FDs or key information are provided.
• All terms follow standard relational theory.

Concept / Approach:
A “determinant” is any attribute set on the left side of a functional dependency. If two attributes together determine another, the pair (A,B) is a determinant, and it is composite because it contains more than one attribute. From (A,B) → C, we cannot infer A → C or B → C unless additional FDs hold.

Step-by-Step Solution:

Verification / Alternative check:
Armstrong’s axioms do not permit decomposing an FD's LHS like (A,B) → C into A → C or B → C in general.

Why Other Options Are Wrong:
A → C / B → C: Not guaranteed; they require additional FDs.
C is a determinant: Not from this FD; C is the dependent attribute.
A alone is always a key: Not implied; keys require uniqueness over all tuples, which is not established.

Common Pitfalls:
Assuming multi-attribute determinants imply each attribute determines the RHS—this is incorrect without further constraints.

Final Answer:
(A,B) is a composite determinant.