4. Consider a schema R = {A,B,C} and the set F of FDs:

F = {AB --> C, C --> B}.

(i) Using the definition of BCNF, explain whether or not R is in BCNF.

(ii) Decompose R into BCNF preserving all dependencies.

5. For this question we are only concerned with 4NF.

No MVD axioms are required in determining the answer.

Consider a schema R = {A,B,C,D,E,I} and the set MF of MVDs and FDs:

MF = {A -->--> BCD, B --> AC, C --> D}.

(i) Explain whether the MVD A -->--> BCD is trivial with

respect to R.

(ii) Decompose R into 4NF. To test your understanding, I insist

that you use the MVD A -->--> BCD first.

6. Prove that any relation scheme R in 3NF with respect to a

set F of FDs must be in 2NF with respect to F.

(Hint: prove by contrapositive, namely, show that

a partial dependency implies a transitive dependency.)

7. Either prove that any relation schema R in 4NF

must be in BCNF or construct a counter-example to show this claim false.

Please provide answers according to question numbers thank you.