(Solution) - Consider the relation REFRIG MODEL YEAR PRICE MANUF PLANT COLOR which is -(2025 Original AI-Free Solution)

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Consider the relation REFRIG(MODEL#, YEAR, PRICE, MANUF_PLANT, COLOR), which is abbreviated as REFRIG(M, Y, P, MP, C), and the following set of 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 LJ1 in Section 15.2.4)