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}

g. [5 points] Show that F is already in canonical cover form.

h. [10 points] 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.

i. [10 points] 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.

j. [10 points] 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.