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Producing more functional dependencies (FDs) from a list of functional dependencies (FDs)

I am currently trying to understand functional dependencies and their properties. I am looking at an example, but when I try to apply the rules I can't see to get the same answers. The question is:

Question: Given a relation T(A,B, C,D) and functional dependencies AB -> C, BC -> D,CD -> A AD -> B What FD’s follow from the given FD’s?

Answer: AD -> CD,AD -> BC,CD -> AB.

When applying the properties of functional dependencies I can't even see how they get the first answer (AD -> CD). If anyone could give me an idea of how we get to the first answer, maybe I can solve the rest myself.

PS: This is NOT homework (as I already have the answer!), but I am revising for an important exam and I need to understand these concepts.


  • $\begingroup$ The thread was closed because someone thought it was homework, when I've made it clear that it is NOT homework because I already have the answers. Any help is appreciated. $\endgroup$ – Alex May 10 '11 at 16:15
  • $\begingroup$ Instead of posting a new duplicated question, here we usually discuss the scope of the original one in meta, and see if there are agreements on reopening it. And this site is for research-level questions in theoretical computer science, normally not included undergrad course materials, whether they are homework or not. $\endgroup$ – Hsien-Chih Chang 張顯之 May 10 '11 at 16:40
  • $\begingroup$ cstheory is for research level questions in theoretical computer science. As you mentioned, this is an undergraduate level question, and thus out of scope. I recommend sites like math.stackexchange.com for undergraduate level questions. $\endgroup$ – Artem Kaznatcheev May 10 '11 at 16:42
  • $\begingroup$ Thanks for letting me know, I didn't realise cstheory was only for research-level questions. Please feel free to help me nonetheless. $\endgroup$ – Alex May 10 '11 at 16:45

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