This is database system concept.

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.Evaluate each of the following as a candidate key for R, giving reasons why it can or cannot be a key: N, NY, NC.

2.Find all the candidate keys of R.

3.Give a lossless-join decomposition of R into Boyce-Codd normal form. Make sure to use the algorithm studied in class (slide 8.46) and to show all details.

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

5.Is R in 3NF?

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

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

8.Use the algorithm we studied in class (slide 8.56) to find a lossless-join and dependency preserving decomposition of R into 3NF. Make sure to show all details.

9.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.

10.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.