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Is the above relation is dependency preserved or not

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This is dependency preserving as C -> D is preserved from indirect FD's.

In Closure set of New relations :

For Relation R2(B,C) : C functionally determines B i.e. C->B

and

For Relation R3(B,D) : B functionally determines D i.e. B->D

Hence if we consider the Union set of FD's of all the decomposed relations :

We can determine (C->B and B->D) hence C->D is obtained.

So we have all the FD's of the original relation with us :

A-> B from R1(A,B)

B-> C from R2(B,C)

C->D from Union set (R1,R2,R3)

and D->B from R3(D,B)

Regards,

Udit
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