First lets write all the dependencies of the subrelation R1(A,B,C,D,F) and R2(B,C,E) in light of the given dependencies ABC --> DEF , BC --> E and C --> B.
Then for R1 , we have :
ABC --> DF and C --> B
For R2 , we have :
C --> B and BC --> E
So the only dependency which we have to check is : ABC --> E (since all other FDs are directly mapped into some subrelation) , which can be done by taking attribute closure of ABC w.r.t FDs of R1 and R2.So,
ABC+ = ABCDEF(as BC --> E is there).
Hence the 1st decomposition is dependency preserving.
We continue the same procedure for 2nd query i.e. 2nd decomposition and find the FD EF --> B is not preserved.Hence it is not dependency preserving decomposition.
Hence , A) option should be the correct option.
