Consider the following set $F$ of functional dependencies on the relation schema $,$ D$.$ E$,$ F$)$:

$AD$

$ABDE$

$BDA$

$ACF$

$($a$)$ List two candidate keys for R$.(6$ points$)$

$($b$)$ Give a lossless dependency preserving $3$ NF decomposition of $r$ based on the set of functional dependencies. $(12$ points$)$

$($c$)$ Give a lossless BCNF decomposition of $r$ based on the set of functional dependencies. Does the decomposition preserve dependencies? Why or why not? $(12$ points$)$