For the universal relation R = {A, B, C, D, E, F, G, H, I, J}, and the set of functional dependencies G = { AB -> C, A -> DE, B -> F, F -> GH, and D -> IJ }, determine if the following two decompositions D1 and D2 are dependency preserving and lossless join decompositions. Show all your work; correct answers alone will not fetch you good scores.

a) 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}.

b) 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}.