What is a candidate key in the context of functional dependencies?

A candidate key is a minimal super key for a relation, meaning it is a set of attributes that uniquely identifies a tuple, and removing any attribute from the set would result in a loss of uniqueness.

Consider a relation R with attributes {A,B,C} and the following functional dependencies:

  1. A→B
  2. A→C

Here, Ais a candidate key because:

  • A determines all attributes (A→B and A→C, which means A→{B,C}).
  • A is minimal; there is no smaller subset of A that has the same property.

If there are multiple sets of attributes that satisfy the candidate key conditions, each of them is considered a candidate key. For example, if R has attributes {A,B,C} and the functional dependency {A,B}→C, then {A,B} might also be a candidate key.

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