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I have this Relation and Functional Dependency:

R = {A, B, C, D, E, G}
FD = E->D 
     C->B 
     CBE->AG 
     B->A 
     G->E

I tried to normalize using 3NF and got:

After minimizing the FDs, I got E->D, C->B, CE->G, B->A, G->E

So resulting decompotision is: {ED, CB, CEG, BA, GE}

Assuming this is correct, CEG is a superkey

Does this mean that this decomposition has lossless join and dependency preserving?

How can I tell if this decomposition also in BCNF?

Lilith X
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  • Please ask 1 question. PS Re "is this right": Show the steps of your work following your reference/textbook, with justification--not all terms/notations are standard & we don't know exactly what algorithm/method you are following & we want to check your work but not redo it & we need your choices when an algorithm allows them & otherwise we can't tell you where you went right or wrong & we don't want to rewrite your reference. [ask] [help] Basic questions are SO faqs, research before considering asking & reflect research in posts. – philipxy Mar 05 '21 at 11:53
  • 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 determine CKs & NFs we must be given FDs that form a cover. Sometimes a minimal/irreducible cover. And the set of all attributes must given. [See this answer.](https://stackoverflow.com/a/53386492/3404097) PS Similarly your preservation "because" only mentions 1 given FD. – philipxy Mar 05 '21 at 11:56
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    Again: 1 question. PS Right now you are just asking for us to rewrite a textbook with a bespoke tutorial & you have shown no research or other effort at answering the question you ask. 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 first place you are stuck. Quote the definitions, theorems, algorithms & heuristics you are relying on. All the steps are also SO faqs. Google with & without 'site:stackoverflow.com'. – philipxy Mar 05 '21 at 12:10

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