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. 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.

2. 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.