If two attributes, P and Q, satisfy the functional dependencies P → Q and Q →…

Concept

A functional dependency X → Y means the value of X uniquely determines the value of Y. When a dependency holds in BOTH directions — X → Y and also Y → X — each attribute set determines the other. Two attribute sets that determine each other this way are called equivalent, and the relationship is described as a mutual (reciprocal) functional dependency.

Application

Here we are told both P → Q and Q → P hold:

• P → Q: knowing P fixes Q.

• Q → P: knowing Q fixes P.

Since each of P and Q determines the other, they reciprocally (mutually) determine one another. This bidirectional determination is exactly a mutual functional dependency; P and Q are equivalent attribute sets.

Contrast with the other dependency types

• Partial dependency: a non-prime attribute depends on only PART of a composite key — a one-way dependency on a key fragment, with no reverse arrow.

• Full functional dependency: a non-prime attribute depends on the WHOLE composite key (not any proper subset) — again strictly one-directional, about a composite key.

• Transitive dependency: an indirect chain X → Y and Y → Z that yields X → Z through an intermediate attribute — a one-way chain, not a pair of attributes that each directly determine the other.

• Multivalued dependency: written X →→ Y, it concerns a SET of values associated with X (a different, non-functional kind of dependency, used for 4NF), not a single-valued determination in both directions.

Only one type captures determination in both directions: a mutual functional dependency.