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I'm currently trouble determining if one of my schemas is in third normal form.

I have a table with columns image_id (A), upload_time (B), uploader_id (C), and image_file (D). A is a key (unique identifier for every row in the table), and BC is also a key (every pair of uploader and upload time is unique). Thus, we have A -> BCD, and BC -> A (and transitively BC -> A through A -> BCD).

Is this table in 3rd normal form? I'm not entirely sure, because I know 3NF allows for a partial key transitive dependency (e.g. XY -> Z, Z -> X), but I'm not sure if it allows for a total key transitive dependency like I have above.

  • "Key FD" is not a clear way to say "FD with a key as determinant". "Key" is not a clear way to say "superkey" or "CK". And which do you mean? "Unique" means superkey, but a CK is an irreducible superkey; unique <> CK. You give FDs via those superkeys, but you don't say the only FDs are those they imply. BC is unique, thus BC->A & D. What does "transitively BC -> A through A -> BCD" mean? Or "allows for"? What "total key transitive dependency"? A->B transitively when there exists X [A -> X -> B and not X->A]. 3NF is iff no non-prime attribute is transitively dependent on a CK. Please clarify. – philipxy Mar 2 '18 at 9:32
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A simple check to see if a relation schema is in Third Normal Form is to see if every left hand side of non-trivial functional dependencies is a superkey (and this test can be used also to check if a relation is in Boyce-Codd Normal Form), or, if this is not the case, if every attribute on the right part is a prime attribute (i.e. part of any candidate key).

So in you case both the dependencies A → BCD and BC → A (and also BC → D) have a candidate key as left part, so the schema is in Third Normal Form (and in this case also in the more strict Boyce-Codd Normal Form).

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