Suppose you are given a database relation R with single$-$valued atomic attributes $($A$,$ B$,$ C$,$ D$,$ E$)$ and a set of functional dependencies F $=\{$AB$->$C$,$ AC$->$B$,$ A$->$E$,$ B$->$D$,$ BC$->$AE$\}$

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

$($b$)$ Name the strongest normal form that holds on R and explain. $(4$ points$)$

$($c$)$ Decompose it into a collection of BCNF relations if it is not in BCNF$.$ Show all steps. $(6$ points$)$