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I have to find a really bad example where you cannot apply Heaths Theorem because of a missing functional dependency.

But am I right, that every relation has at least one functional dependency?

Or can anyone of you come up with an example table with at least 3 Sets of Attributes to project it and then join it together. The result should of course be different from the original table to proof Heath's Theorem right (no FD -> no lossless decompositions)

It does not matter, wheter it is an sql example or an abstract one.

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I know this is no relevant question for programmers, because such an example would never be considered practically relevant. But the proof alone is not enough for my Prof. :( –  BackfromHell Dec 3 '13 at 12:30
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migrated from stackoverflow.com Dec 3 '13 at 17:44

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But am I right, that every relation has at least one functional dependency?

Relation can has no functional dependencies, if it has no non-key attributes, i.e. it is full-keyed relation.

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You should strike through that incorrect sentence where you say "yes, I believe". Then what remains is the correct answer. –  Erwin Smout Jan 3 at 22:46
    
@Erwin Smout, I have done. –  msi77 Jan 4 at 6:42
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