Partial Dependency(Databases)

Question

I need closure on this. I fabricated a definition that partial dependency is when fields are indirectly dependent on the primary key or partially dependent but are also dep

Answer 1

If there is a Relation R(ABC)

-----------
|A | B | C |
-----------
|a | 1 | x |
|b | 1 | x |
|c | 1 | x |
|d | 2 | y |
|e | 2 | y |
|f | 3 | z |
|g | 3 | z |
 ----------
Given,
F1: A --> B 
F2: B --> C

The Primary Key and Candidate Key is: A

As the closure of A+ = {ABC} or R --- So only attribute A is sufficient to find Relation R.

DEF-1: From Some Definitions (unknown source) - A partial dependency is a dependency when prime attribute (i.e., an attribute that is a part(or proper subset) of Candidate Key) determines non-prime attribute (i.e., an attribute that is not the part (or subset) of Candidate Key).

Hence, A is a prime(P) attribute and B, C are non-prime(NP) attributes.

So, from the above DEF-1,

CONSIDERATION-1:: F1: A --> B (P determines NP) --- It must be Partial Dependency.

CONSIDERATION-2:: F2: B --> C (NP determines NP) --- Transitive Dependency.

What I understood from @philipxy answer (https://stackoverflow.com/a/25827210/6009502) is...

CONSIDERATION-1:: F1: A --> B; Should be fully functional dependency because B is completely dependent on A and If we Remove A then there is no proper subset of (for complete clarification consider L.H.S. as X NOT BY SINGLE ATTRIBUTE) that could determine B.

For Example: If I consider F1: X --> Y where X = {A} and Y = {B} then if we remove A from X; i.e., X - {A} = {}; and an empty set is not considered generally (or not at all) to define functional dependency. So, there is no proper subset of X that could hold the dependency F1: X --> Y; Hence, it is fully functional dependency.

F1: A --> B If we remove A then there is no attribute that could hold functional dependency F1. Hence, F1 is fully functional dependency not partial dependency.

If F1 were, F1: AC --> B;
and F2 were, F2: C --> B; 
then on the removal of A;
C --> B that means B is still dependent on C; 
we can say F1 is partial dependecy.

So, @philipxy answer contradicts DEF-1 and CONSIDERATION-1 that is true and crystal clear.

Hence, F1: A --> B is Fully Functional Dependency not partial dependency.

I have considered X to show left hand side of functional dependency because single attribute couldn't have a proper subset of attributes. Here, I am considering X as a set of attributes and in current scenario X is {A}

-- For the source of DEF-1, please search on google you may be able to hit similar definitions. (Consider that DEF-1 is incorrect or do not work in the above-mentioned example).