Consider the relation R = {A, B, C, D, E, F, G, H, I} and the set of functional dependencies {AB C, A DE, B F, F G, D HI}.

For each of the following decompositions of R, determine whether it has (i) the lossless join property; and (ii) which normal form each relation is in.

(a) D = {R1, R2, R3, R4, R5}, with R1 = {A, B, C}, R2 = {A, D, E}, R3 = {B, F}, R4 = {F, G}, R5 = {D, H, I}.

(b) D = {R1, R2, R3, R4, R5}, with R1 = {A, B, C, D}, R2 = {D, E}, R3 = {B, F}, R4 = {F, G, H}, R5 = {D, H, I}.