$3$ Given the Relation R$($A$,$B$,$C$,$D$,$E$,$M$)$ and F $=\{$A$->$B$,$ A$->$C$,$ CD$->$E$,$ CD$->$M$,$ B$->$E$\}$

$($a$)$ Is A$->$BC implied by F$?$ Explain your answer.

$($b$)$ What is the attribute closure of A wrt F$?$ Attribute closure of A is denoted by A$+$ and

initially A$+=\{$A$\}$

$($c$)$ Is attribute A a key $($candidate key$)$ for R $($based on F$)?$ How would you find that out?

$($d$)$ Is AB a key for R$?$ Explain your answer.

$($e$)$ Is AD a key for R$?$ Explain your answer, make sure that you check the minimality

property.