Consider the relation schema R$($A$,$ B$,$ C$,$ D$,$ E$,$ G$)$ with functional dependencies

F $=\{$AB$->$C$,$ AG$->$E$,$ B$->$D$,$ E$->$G$\}.$

Notice F is the minimum cover of itself. For each of the following decompositions

R$($A$,$ B$,$ C$,$ D$,$ E$,$ G$),$ determine whether it is $($a$)$ dependency$-$preserving, and $($b$)$ lossless.

$1\mathrm{.}1.\{$ABC$,$ CDE, EG$\}$