For the following relation and functional dependencies, analyze the potential decompositions and show if they are lossless decompositions.

Relation R = (A, B, C, D, E) where A might represent Voter ID Number, B as Voter Address, C Name, D State, E License Plate Number. The key of R is ABE and the functional dependencies of R include:

ABC

DEC

BD

D1) ABDE, ABC

D2) ABC, DE

D3) AB, DEC

D4) ABE, CDE

D5) ACD, BCE

D6) ABCD, EC

D7) ABCD, DC

D8) ABCE, BD

Assuming we have a partial (binary) decomposition already performed and have ABCE remaining as one table (with all the initial functional dependencies). ABCE violates 2NF and needs to be decomposed further. Analyze the following decompositions of ABCE and show if they are lossless decompositions.

D1) ABC, DEC

D2) ABC, ABE

D3) ABE, DEC

Assuming we have a partial (binary) decomposition already performed and have ABDE remaining as one table (with all the initial functional dependencies). ABDE violates 2NF and needs to be decomposed further. Analyze the following decompositions of ABDE and show if they are lossless decompositions.

D1) ADE, BD

D2) ABE, BD

What are all possible 2NF decompositions of ABCDE which satisfy the lossless (nonadditive) join property?