1. Consider the relation R(MODEL#, YEAR, PRICE, MANUFACTURER, COLOR), which is abbreviated as R (M, Y, P, N, C), and the following set of F of functional dependencies: F={M -> N, {M,Y} -> P, N -> C}

1. Evaluate each of the following as a candidate key for R, giving reasons why it can or cannot be a key: {M}, {M,Y}, {M.C}
2. Based on the above key determination, state whether the relation R is in 3NF and in BCNF, giving proper reasons.
3. Consider the decomposition of R into D={R1(M,Y,P), R2(M,N,C)}. Is this decomposition lossless? Show why.
4. Consider the same decomposition in (c). Does this decomposition preserve dependencies? Show why.