Consider the relation REFRIG(Model#, Year, Price, Manuf_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} 

 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}. 

Based on the above key determination, state whether the relation REFRIG is in 3NF and in BCNF, giving proper reasons. 

Consider the decomposition of REFRIG into D = {R1(M, Y, P), R2(M, MP,C)}. Is this decomposition lossless?