Can A and B be functionaly dependent on each other?

Question

If B is functionally dependent on A (A -> B) can A be functionally dependent on B (B -> A)? Why?

Example:

A table contains five columns: Patient Number, Full name, Bed number, Ward number and Ward name.

Is it possible to say that Ward Number -> Ward Name and Ward Name -> Ward Number?

From my understanding a functional dependency A -> B means that given a tuple containing A there will always be the same B, but not the other way around.

A Ward will always have the same number and name making the functional dependency go both ways.

Answer 1

If B is functionally dependent on A (A -> B) can A be functionally dependent on B (B -> A)?

Yes. Informally, it might help you to think about it this way.

Say a relation has two candidate keys, A and B. Since A is a candidate key, it determines all the other attributes. So A->B. And since B is a candidate key, it also determines all the other attributes. So B -> A.

For a real-world example, think about a table of chemical elements. (WARNING: I'm not a chemist.)

element_name  atomic_number  chem_symbol
--
Hydrogen      1              H
Helium        2              He
Lithium       3              Li
...

Each of these three columns is a candidate key. And element_name determines atomic_number and chem_symbol, atomic_number determines element_name, and chem_symbol, etc.