Consider the relation REFRIG(Model#, Year, Price, Manu plant, Color), which is abbreviated as REFRIG(M, Y, P, MP, C), and the following set F of functional dependencies: F = {M → MP, {M, Y} → P, MP → C}
a. Evaluate each of the following as a candidate key for REFRIG, giving reasons why it can or cannot be a key: {M}, {M, Y}, {M, C}.
b. Based on the above key determination, state whether the relation REFRIG is in 3NF and in BCNF, giving proper reasons.
c. Consider the decomposition of REFRIG into D = {R1(M, Y, P), R2(M, MP, C)}. Is this decomposition lossless? Show why. (You may consult the test under Property NJB in Section 16.2.4.)