$3.(40$ points$)$ Consider a relation schema R$3($A$,$ B$,$ C$,$ D$,$ E$)$ that satisfies the set of functional

dependencies F$3=\{$A $$ BC$,$ AC $$ BD$\}.$

$1)(5$ points$)$ Calculate $($AC$)+$ and $($AE$)+$

$2)(5$ points$)$ Is AB $$ C in F$3+?$ Justify your answer.

$3)(15$ points$)$ Find the canonical cover Fc of F$3.$

$4)(15$ points$)$ Is R$3$ in $3$NF$?$ Explain the reason to your answer. If R$3$ is not in $3$NF$,$ give a

lossless$-$join, dependency preserving $3$NF decomposition of R$3.$