1. Suppose we have relation R (ABCDE) and R1(ABC), R2(BCD) and R3(ACE) be a decomposition of R. Let F= {AD, BD, CDE}.

a. Use the chase test to tell whether this decomposition of R is lossless.

b. Is this decomposition dependency preserving?

c. Is this decomposition in BCNF? If not, indicate all BCNF violations and try to decompose R into BCNF.

2. Let R(ABCDE) be a relation and F= {ABC, CD}. Let R1(ABC), R2(ADE) be a decomposition of R

a. Is this decomposition lossless?

b. Is this decomposition dependency preserving?

c. Is this decomposition in BCNF?

d. Can you decompose R into dependency preserving decomposition which is in BCNF?

3. Let R(ABCDE) be a relation and F={AB, BCE, and ED A}. Decompose R into BCNF.

4. Let R(ABCDEFGH) be a relation and F= {ABE, CD, DE, FGA}. Decompose R in BCNF.

Is your decomposition dependency preserving?