##### Whether the following functional dependencies : A → B, B → C, C → D and D → B is dependency preserving?

Let R (A, B, C, D) be a relational schema with the following functional dependencies :

A → B, B → C, C → D and D → B. The decomposition of R into (A, B), (B, C), (B, D)

how this relation is dependency preserving i am not able to get C->D ?

After decompostition,

(A,B) will have A->B

(B,C) will have B->C and C->B

(B,D) will have B->D and D->B

Now if you take union of all the FD's, you will get C->D by taking closure of C from the union.