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I am stuck in this question. What should be the answer to this:

The relation scheme Student Performance (name, courseNo, rolINo, grade) has the following functional dependencies:
name, courseNo, -> grade
rolINo, courseNo -> grade
name -> rolINo
rolINo -> name

The highest normal form of this relation scheme is

(a) 2 NF (b) 3 NF (c) BCNF (d) 4 NF

philipxy
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Mehul Jain
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    If you're going to post an obvious homework/test problem, at least make an *effort* to answer it yourself and give your reasoning. – Damien_The_Unbeliever Aug 18 '14 at 07:28
  • 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 rely on. All the steps are also SO faqs. Google with & without 'site:stackoverflow.com'. – philipxy Dec 13 '21 at 12:09
  • 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 be given. [See this answer.](https://stackoverflow.com/a/53386492/3404097) – philipxy Dec 13 '21 at 12:17

2 Answers2

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Relation has 2 overlapping candidate-key dependencies so it is in 3nf.

Ank
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  • there is a visible transitivity (name-to-roll,roll-to-name). Hence it should be in 2nf .....?? Am I wrong somewhere?? – Mehul Jain Aug 19 '14 at 12:03
  • I think name is not ck and roll is part of ck obviously.So name-roll and roll-name are O.C.D.s.It is not transitivity because for transitive dependency determinant should be non prime attribute.But in this case both roll and name are prime attributes. – Ank Aug 19 '14 at 14:57
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The Answer is 3NF

  1. name, courseNo, -> grade,
  2. rolINo, courseNo -> grade,
  3. name -> rolINo,
  4. rolINo -> name, first 2 i.e 1 and 2 follows BCNF as LHS is superkey in both. but 3rd and 4th do no follow BCNF so 3 NF as rollNo and name both in RHS are prime attributes. they follow 3NF.

Now, answer for the comments about transitivity, definition of transitive dependency is if A -> B and B -> C

then A -> C is the transitive dependency and our goal is remove such, i.e we want to keep A->B and B->C in different tables, so that there will be no transitive dependency for more clarification refer

Protonic RED
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  • This is full of wrong reasoning & wrong & unclear statements. Same thing for the link you give. See my comments on the question. – philipxy Dec 13 '21 at 12:17