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DBMS Functional Dependency

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Let us come to the statements one by one..

Statement one is not necessarily true as functional dependency can have have two meanings..

A many one to relation exists 

(or)

One to one relation exists.

Since in X --> Y we require that for a X we have unique Y..But X in the relation can also be unique..So one to one relation may also exist . So A) is not necessarily true always.

So option B) is violated obviously..

Option C) is also false we can have implied dependency in a subrelation that can be found using attribute closure of the attributes of the subrelation but with respect to original FD set..So it is not sufficient that only those FDs which can be directly mapped into subrelations will lead to dependency preservation as all FDs of original may not be directly mapped into subrelations and still the dependency preservation may hold..

Hence option D) is correct option. 

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