Is a functional dependency (FD) an equation, or is it a semantic constraint about attribute values?

Introduction / Context:
Functional dependencies express how attribute sets determine other attribute sets. The question claims an FD is “always an equation,” which is a misunderstanding of its nature.

Given Data / Assumptions:

• An FD is written X → Y, indicating that tuples agreeing on X must agree on Y.
• It is a logical/semantic constraint, not arithmetic or algebraic equality.
• FDs guide normalization (2NF, 3NF, BCNF).

Concept / Approach:
FDs are not equations; they do not equate values or expressions. They assert dependence: X values functionally determine Y values. While sometimes one writes Y = f(X) informally, that is a conceptual mapping, not an equation to be solved. Thus, calling FDs “equations” is incorrect.

Step-by-Step Solution:

Verification / Alternative check:
Review Armstrong’s axioms (reflexivity, augmentation, transitivity) that manipulate dependencies, not arithmetic equalities.

Why Other Options Are Wrong:

• References to normal forms or numeric keys do not convert constraints into equations.

Common Pitfalls:
Confusing functional dependence with mathematical functions in the algebraic sense and treating schema constraints as expressions to solve.

Final Answer:
Incorrect