Functional Dependencies and Normalization $[20$ points$]$

Consider the relation schema R $=($A$,$ B$,$ C$,$ D$,$ E$,$ F$)$ and the set of functional

dependencies F: A$->$B$,$ A$->$C$,$ BC$->$E$,$ BC$->$D$,$ E$->$F$,$ BC$->$F

Note that in all the following, you will never have to compute F$+,$ the closure of

F$!$

a$.$ List the minimal candidate key$($s$)$ for R$.$ Write $$none$$ if you think there

are no candidate keys. $[2$ points$]$

b$.$ List the FDs in F that violate BCNF$.($Hint: There are four$)[4$ points$]$

c$.$ Is R in $3$NF $($yes or no$)?[2$ points$]$

d$.$ Is F a minimal cover?$[2$points$]$