Consider the schema $R=(A,B,C,D,E,G)$ and the set of functional dependencies:

$ABCD$

ADE$$GDE

$BGC$

$GDE$

Answer the questions:

a$)B^{+}=?$

b$)$ Is $B$ a superkey?

a$)A^{+}=?$

b$)$ Is $A$ a superkey?

a$)(AB{)}^{+}=?$

b$)$ Is $AB$ a superkey?

c$)$ Is $AB$ a candidate key?

Find the candidate keys of $R.$

a$)$ Is $R$ in BCNF$?$ Why or why not?

b$)$ Is $R$ in $3$NF$?$ Why or why not?

Find a canonical cover for $F$

Use a $3$NF decomposition algorithm to generate a $3$NF decomposition of $R$