Given relation $R2(A,B,C,D,E,F,G)$ and the set of functional dependencies

$B,C,DA$

$B,CE$

$AF$

$FG$

$CD$

$AG$

Show that $($B$,$C$)$ could be a key of R$2.(1$ mark$)$

Is $R2$ in $2NF?$ Justify your answer. If not decompose to $2NF.(2$ marks$)$

Is R$2$ in $3NF?$ Justify your answer. If not decompose to $3NF.(2$ marks$)$

Check whether your decomposition satisfies BCNF normal form. $(1$ mark$)$