$3.[12$ points$]$ Consider a relation R $=($A$,$ B$,$ C$,$ D$,$ E$,$ F$)$ and a set S $=\{$AB $$ C$,$ AC $$ B$,$ AD $$ E$,$ B $$ D$,$ BC $$ A$,$ D $$ E$\}$ of functional dependencies that hold over R$.$ Assume that R was decomposed into R$1($B$,$ D$,$ E$,$ F$)$ and R$2($A$,$ B$,$ C$)$ and that S$1$ is the set of functional dependencies that hold over R$1$ and S$2$ is the set of functional dependencies that hold over R$2.$

$3\mathrm{.}1.[7$ points$]$ Compute S$2,$ the projection of S on relation R$2.$ Show your work.

$3\mathrm{.}2.[5$ points$]$ Provide a key for R$2($A$,$ B$,$ C$)$ with respect to the set of functional dependencies S$2$ you calculated in part $3\mathrm{.}1.$ Show your work.