a Given a relation schema $R=\{A,B,C,D,E,F,G\}.$ Find the keys of $R$ and then

decompose $R$ into highest normal form for the following functional dependencies :

i$)F=\{ABC,FG,ADE\}$

ii$)F=\{BDEF,ADG,ABC\}$

b Given a relation schema $R=\{A,B,C,D\}$ and a set of functional dependencies $F.$

Determine whether the decomposition of $R$ is producing lossless or lossy join for the

following decompositions $D$ :

i$)D=\{R1,R2\}$ where, $R1=\{A,B\},R2=\{C,D\}$ and $F=\{AB,CD\}$

ii$)D=\{R1,R2,R3\}$ where, $R1=\{A,B\},R2=\{B,C\},R3=\{B,D\}$ and

$B,BC,CD,DB$