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Consider relation R(A,B,C,D,E). The following functional dependencies are assumed to hold over R:

  • A -> B, C
  • B -> D

What is a key of R? If there are multiple candidate keys list all.

I think there is missing FD, but not sure can any one help and also decompose to 3NF.

The Impaler
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Maho
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    What kind of notation is this? – Evert Oct 17 '21 at 18:03
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    Right now you are just asking for us to rewrite a textbook with a bespoke tutorial & do your (home)work & you show no research or other effort. Please see [ask], hits googling 'stackexchange homework' & the voting arrow mouseover texts. Show the steps of your work following a textbook/reference with justification & ask 1 specific researched non-duplicate question re the 1st place you are stuck/unsure. Quote definitions, theorems, algorithms & heuristics you are relying on. All the steps are also SO faqs. Google with & without 'site:stackoverflow.com'. – philipxy Oct 17 '21 at 18:38
  • Your "I have these FDs" doesn't make sense. "These are all the FDs that hold"?--Not possible. "These are all the non-trivial FDs that hold"?--Not possible. "These are some FDs that hold"?--Question can't be answered. Find out what a *cover* is & what the exact conditions are to apply a particular definition/rule/algorithm. To find CKs & NFs we need FDs that form a cover. Sometimes a minimal/irreducible cover. And the set of all attributes must be given. [See this answer.](https://stackoverflow.com/a/53386492/3404097) PS Please read & act on the edit help re block quotations & line breaks. – philipxy Oct 17 '21 at 18:39
  • Please clarify your specific problem or provide additional details to highlight exactly what you need. As it's currently written, it's hard to tell exactly what you're asking. – Community Oct 18 '21 at 08:42

1 Answers1

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I am assuming that the two dependencies are a cover of the dependencies of R. In this case, the only candidate key is {A, E}.

A decomposition in 3NF arising from the classical synthesis algorithm is the following:

R1 (A, B, C)

R2 (B, D)

R3 (A, E)

Renzo
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