Suppose a relational schema R$2($A$,$ B$,$ C$,$ D$,$ E$,$ F$,$ G$,$ H$,$ I$)$ and set of functional dependee: $\{$ A$,$B C $($

Suppose a relational schema R$2($A$,$ B$,$ C$,$ D$,$ E$,$ F$,$ G$,$ H$,$ I$)$ and set of functional dependencies

$\}$

$A,DG,H$

$B,DE,F$

$AI$

$\{HJ$

Identify all candidate keys for $R2.$

ABD is the candidate key, because closure of ABD has all the attributes of R$.$ Prime attributes: A B D$,$ Non$-$prime attributes: C E F G H I

Check out that $R2$ is in $3NF$ or not? If not decompose it in $3NF.$

$(1)--$ Neither $AB$ is super key, nor $C$ is prime attribute.

$(2)--$ Neither AD is not super key, nor GH is prime attribute.

$(3)--$ Neither BD is not super key, nor EF is prime attribute.

$(4)--$ Neither $A$ is not super key, nor I is prime attribute.

$(5)--$ Neither $H$ is not super key, nor $J$ is prime attribute.

$So,R2$ is not in $3NF$ as it is not following the rules of $3NF.$

Therefore, R$2($A$,$B$,$C$,$D$,$E$)$ needs to be divided into following:

R$21($A B C I$)$

R$22($A D G H J$)$

R$23($B D E F$)$

R$24($A B D$)$

R$211($A B C$)$

R$212($A I$)$

R$221($A D G H$)$

R$221($H J$)$

END OF EXAM$1)$A$,$D G$,$HB$,$D E$,$FA IH J $\}$