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: $,Y$

Find the candidate keys.

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

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

$12$pt $vv$ Paragraph $vv||$ B $I{?}_{,}{A}_{?}.$