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Consider a relation R(A,B,C,D,E) and the only FDs,

ABD->C

BC->D

CD->E

These are the only 3 FDs. I want to know if the above relation is in 2NF or not.

According to the definition of 2NF, a relation to be in 2NF, it should be in 1NF and it should not have partial dependency.

But I'm not getting the partial dependency concept.

Somewhere it's written that when a proper subset of a key determines a non-prime attribute then it is partial dependency.

Somewhere it's written that when a prime attribute which is not a key determines a non-prime attribute then it is partial dependency.

Because of these 2 different definitions I'm getting confused.

Please help.

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  • $\begingroup$ Same comments apply after your edit, please act on them. How to Ask help center Computer Science Meta Meta Stack Exchange $\endgroup$
    – philipxy
    Jan 21 at 14:27
  • $\begingroup$ All your definitions are wrong. What is your textbook name & edition? (Though they can be very poor.) PS "These are the only 3 FDs." cannot be. When some FDs hold, others do--per Armstrong's axioms. Others might hold too. To determine CKs & NFs we must be given FDs that form a cover. And the set of all attributes. See this answer. PS "1NF" has many meanings. What's yours? PS Partial Dependency (Databases) PS Ask 1 question, re where you're 1st stuck. $\endgroup$
    – philipxy
    Jan 21 at 14:50
  • $\begingroup$ @philipxy I'm referring books of Henry Korth and Ramakrishnan. $\endgroup$ Jan 21 at 14:57
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    $\begingroup$ Please clarify via edits, not comments. Please put what is need to ask in your post including quotes. Please ask exactly 1 clear specific researched non-duplicate question. PS Name & edition & quotes. $\endgroup$
    – philipxy
    Jan 21 at 15:09
  • $\begingroup$ The definition of partial FD in Korth et al is correct. The definition in Ramakrishnan et al is not complete; they only tell you when a FD of the form set->attribute that violates 3nf is partial. (Their definition of transitive FD has the same problem.) (The definition of transitive FD in Korth et al is not complete; they only tell you when a FD of the form set->attribute is transitive.) Pick a textbook & follow it. $\endgroup$
    – philipxy
    Jan 22 at 5:36
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Second normal form means that each non prime attribute must not depend on a proper subset of a candidate key.

In your example, assuming that the given FDs are a cover of the FDs of the relation, you have two candidate keys, ABC and ABD. Moreover, the attribute E depends on BC, which is a proper subset of the candidate key ABC (you can verify this by computing the closure of BC, BC+, and see that E belongs to that closure).

So the relation is not in 2NF.

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  • $\begingroup$ Thank you so much $\endgroup$ Jan 21 at 16:14

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