Dependency Preserving or Not ?

Question

R(ABCD)

F={  A→B, B→C, C→D, D→A }

Now Decompose this into D={ AB, BC, CD }

Dependency is preserved or Not ?

Source : http://www.gatecrack.in/following-decomposition-dependency-preserving-not/

Comments

Yes Dependency preserved. D-->A we can derive by combining AB,BC and CD via transitive dependency.

Answer 1

No,dependency is not preserved because FD D->A is not preserved if relation is decomposed as given.

Comments

Thanks

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Can u pls explain in details how to check for it ?

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D -> A preserve. via indirect FD

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Dependency is preserved. Check this link 

https://gateoverflow.in/741/gate2001-2-23