Q$3\mathrm{.}1(6$ points$)$ Determine whether each of the following FDs is implied by the FDs above:

$($a$)$ $EF $\backslash$rightarrow BC$

$($b$)$ $BC $\backslash$rightarrow BF$

$($c$)$ $DEF $\backslash$rightarrow AB$

$($d$)$ $DF $\backslash$rightarrow AE$

$($e$)$ $CD $\backslash$rightarrow ED$

$($f$)$ $DE $\backslash$rightarrow AF$