Homework # 13

1. Given: R( A, B, C, D, E, F, G, H, I, J )

F = { AB ® C, A ® DE, B ® F, F ® GH, D ® IJ }

Determine whether each decomposition has the lossless join property with respect to F.

a) R1( A, B, C)

R2( A, D, E)

R3( B, F )

R4( F, G, H )

R5( D, I, J )

2. R1( A, B, C, D, E)

R2( B, F,G, H )

R3( D, I, J )

3. R1( A, B, C, D)

2. Given R(A,B,C) with the data as shown in the table that follows:

R: A B C

w x p

w x q

z x p

z x q

w y q

z y p

Explain and/or demonstrate your answer to the following questions (a simple yes or no will not suffice).

a) Does the multi-valued dependency (MVD) B->>C hold? Explain.

b) Can R be lossless 2-decomposed? Explain.

c) Can R be lossless 3-decomposed? Explain.

d) Is R in 4NF? Explain.

e) Is R in 5NF? Explain.