Consider the relation schema R = (N, Y, P, M, C) and assume that the following set of functional dependencies hold on R: F = { N M, NY P, M C} The letters can be interpreted as follows: R = (Model_Number, Year, Price, Manufacturing_Plant, Color).

1.Give a lossless-join decomposition of R into Boyce-Codd normal form. Make sure to use the algorithm to show all details.

2.Does your decomposition preserve functional dependencies? Justify your answer.

3.Is R in 3NF?

4.Show that the functional dependency NY P does not contain extraneous attributes.

5.Show that F is already in canonical cover form.

6.Use the algorithm to find a lossless-join and dependency preserving decomposition of R into 3NF. Make sure to show all details.

7.Consider the decomposition d = (R1, R2) where R1 = (N, Y, P) and R2 = (N, M, C). Is this decomposition lossless-join? Make sure to justify your answer and to show all details.

8.Consider the decomposition d = (R1, R2, R3) where R1 = (N, M), R2 = (M, C) and R3 = (P, Y). Is this decomposition dependency preserving? Make sure to justify your answer and to show all details.