$3.3$NF Consider a relation schema R with attributes ABCDEF with functional dependencies S:

S $=\{$AB $->$ BCDE, C $->$ D$,$ CDF $->$ AD$,$ DE $->$ C$,$ CD $->$ E $\}$

$($a$)$ Compute a canonical cover for S$.$ In your final answer, put the FDs into alphabetical order.

$($b$)$ Using the canonical cover from part $($a$),$ employ the $3$NF synthesis algorithm to obtain a losslessand dependency$-$preserving decomposition of relation R into a collection of relations that are in $3$NF$.$

$($c$)$ State which of your decomposited relations are in BCNF$.$

$($d$)$ List all candidate $($minimal$)$ keys for R$.$