GATE 1997-2.7 Small change in given data

Question

Consider the schema R = (S T U V) and the dependencies S → T, T → U, U → V and V → S. Let R = (R1 and R2) be a decomposition such that R1 ∩ R2 = ϕ. (In the actual gate question it was R1∩R2 ≠ ϕ) The decomposition is:-  

1. not in 2NF
2. in 2NF but not 3NF
3. in 3NF but not in 2NF
4. in both 2NF and 3NF

Comments

If the decomposition leads to lossy, then we don't decompose them i think.

Answer 1

answer is LOSSY decomposition

Comments

I am trying to say that

1. decomposing a table into 3NF decomposition
2. decomposing a table into lossless decomposition
3. decomposing the tables into dependency preserving decomposition

are 3 different things.

A decomposition may or may not follow all the 3 conditions togather.

Like we can't say "if we decompose a table into 3 NF then it will definitely be lossless or it will definitely be dependency preserving."

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@Satbir then what about the fact that every 3NF decomposition is lossless and dependency preserving ?

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can you give me any reference for the above comment.

Every 3NF is not DP and lossless ...we can break a Relation in such a way that it follows all the 3 conditions.

https://gateoverflow.in/21210/bcnf-and-3nf

read comments and the best answer .