Relation: x=(d,b,c,f,g,h) Functional dependencies: d→bc,g→hd Decomposed into: a=(d,b,c)Consider relation R(A,B,C,D,E,F,G)

First reduce the dependencies to a minimal-cover form. Splitting RHS attributes and removing redundant parts gives the useful dependencies:
AD→B, CD→E, CD→G, E→D, F→C, D→F.

Lossless join check:
The decomposed relations are R1(A,B,C,D,E) and R2(A,D,F,G).
Their common attributes are {A,D}.

Compute {A,D}+ using the dependencies:
AD→B gives B.
D→F gives F.
F→C gives C.
Now C and D are available, so CD→E gives E and CD→G gives G.
Thus {A,D}+ = {A,B,C,D,E,F,G}.

Since the common attributes {A,D} determine all attributes, the decomposition is lossless.

Dependency preservation check:
Some dependencies are preserved in the projections, but CD→G is not. C and D are in R1, while G is in R2, and the projected dependencies cannot derive G from CD without joining the relations. Therefore the decomposition is not dependency preserving.

Hence, the decomposition is lossless and not dependency preserving. Option D is correct.