Given a relation R $($A$,$ B$,$ C$,$ D$).$ Answer the following questions

with the given set of FDs: $(1)$ identify candidate keys and $(2)$ state the strongest normal form that R satisfies $($e$.$g$.,1$NF$,2$NF$,3$NF$,$ or BCN$)$

$($a$)$ FDs: A $->$ B$,$ A $->$ C$,$ BC $->$ D

$($b$)$ FDs: AB $->$ CD$,$ CD $->$ AB

$($c$)$ FDs: AD $->$ B$,$ BD $->$ C

$($d$)$ FDs: AB $->$ C$,$ BC $->$ D$,$ CD $->$ A

$($e$)$ FDs: A $->$ B$,$ B $->$ C$,$ C $->$ D$,$ D $->$ A