3. Nonadditive (Lossless) Join Property (24 pts).

R = {ABCDEFGHIJ}

F = { AB -> C

A -> DE

B -> F

F -> GH

D -> IJ

}

Determine whether each decomposition into R1 and R2 has the lossless join property. Be sure to state why or why not.

a. R1(ABC) and R2(ABDEFGHIJ)

b. R1(ADE) and R2(EBCFGHIJ)

c. R1(BFDIJ) and R2(ABCDEFGH)

d. R1(BDFGHIJ) and R2(ABCDE)