I have a relation:
R = {A, B, C, D, E, F, G, H, I, J}
And a set of functional dependencies:
G = {AB -> C, A -> DE, B -> F, F -> GH, and D -> IJ}
I ended up decomposing into two decompositions.
D1 = {R1, R2, R3, R4, R5}
R1 = {A, B, C}
R2 = {A, D, E}
R3 = {B, F}
R4 = {F, G, H}
R5 = {D, I, J}
D2 = {R1, R2, R3, R4, R5}
R1 = {A, B, C, D}
R2 = {D, E}
R3 = {B, F}
R4 = {F, G, H}
R5 = {D, I, J}
How can I prove that D1, D2 are dependency preserving and lossless join decompositions?
Related question that got me as far as the decompositions but I am lost. 2NF decomposition + database normalization
A->DE
information is not preserved.