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If the functional depencies are
AB-->CD
BC-->D
IS the relation still in 2NF?,I mean since AB is the key and the 2nd BC,out of which B is part of the key,is the relation still in 2NF??

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Can't BC->D be shortened to C->D since AB->C? – Petter Brodin Jan 19 at 11:05

2 Answers

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Assuming your relation is ABCD and assuming you meant the following functional dependencies:

  • AB-->C
  • BC-->D

Then you need to decompose this relation to get it to third normal form (3NF). This is because D is not determined by the key of ABCD. To bring this to 3NF you need to have two relations: ABC and BCD. Now each non-key attribute is fully dependent on the key of its relation (and nothing else).

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Shouldn't you explain why/how you removed the AB->D dependency? – ypercube Jan 19 at 13:27
@ypercube, I thought about that and thought that it was probably a typo based on short-cutting the listing of the original relation (ABCD). It seemed pretty unlikely that D is determined by both AB and BC. Why not write ABC-->D? I couldn't think of a practical case that met the dependencies as stated. – Joel Brown Jan 19 at 13:35
Oh, I thought you meant that we can derive AB->D from the other 2 dependencies. – ypercube Jan 19 at 13:36
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From wikipedia, 2nd Normal Form:

Second normal form (2NF) is a normal form used in database normalization. 2NF was originally defined by E.F. Codd in 1971. A table that is in first normal form (1NF) must meet additional criteria if it is to qualify for second normal form. Specifically: a table is in 2NF if and only if it is in 1NF and no non-prime attribute is dependent on any proper subset of any candidate key of the table. A non-prime attribute of a table is an attribute that is not a part of any candidate key of the table.

There is only one candidate key, the AB.

About the other two non-prime attributes, C and D:

  • C depends only on the candidate key AB.

  • D depends on on the candidate key AB and on BC. BC is neither a candidate key nor a proper subset of (the only one) candidate key. (It doesn't matter that B is a subset of the candidate key, because D does not depend on just B.)

So, the relation is in 2NF.

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