Question B$.[50$ marks$]$

Consider the relation $R=\{A,B,C,D,E,F,G,H,$I,$J\}$ and the set of functional

dependencies $F=\{\{A,D\}\{C\},\{A\}\{B,E\},\{D\}\{F\},\{F\}\{G,H\},\{B\}\{I,J\}\}.$

Prove that $\{A\}\{B,J\}$ holds by using inference rules. $(10$ marks$)$

Is $\{A,B,D\}$ a superkey? Is $\{A,D,E\}$ a candidate key? Why? $(10$ marks$)$

Is $\{C,D\}$ a superkey? Is $\{C,D\}$ a candidate key? Why? $(10$ marks$)$

Decompose R into $2$NF$.(10$ marks$)$

Decompose R into BCNF$.(10$ marks$)$