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