Given the schema $S=($:$\{A,B,C,D,E,G,H\},F$:$),$ where $F$ represents the following dependencies:

$GBD$

$GD$

$EB$

$BH$

$HC$

$EC$

$EBAH$

$EA$

i$.$ Find a minimal cover for this schema.

ii$.$ Find a key for this schema.

iii. Find a third normal form decomposition for this schema.

iv$.$ Find a BCN form decomposition for this schema.

v$.$ Determine whether the following decompositions are lossy or lossless.

$R1=\{E,C,B\}R2=\{D,H,E,G,A\}$

$R1=\{H,B\}R2=\{C,D,E,A,G,B\}$

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