Q$7.$ Consider the relation $R=\{A,B,C,D,E,F,G,H,$I,$J,K,L,M,N\}$ and the set of functional

dependencies $,$

$\{D\}\{G,H\}.$

$($a$)(2\%)$ What is the key for $R?$

$($b$)(6\%)$ Decompose $R$ into $2NF,$ then $3NF$ relations.Consider the relation R $=\{$A$,$ B$,$ C$,$ D$,$ E$,$ F$,$ G$,$ H$,$ I, J$,$ K$,$ L$,$ M$,$ N$\}$ and the set of functional dependencies F $=\{\{$A$,$ B$,$ C$\}->\{$L$\},\{$B$\}->\{$D$,$ E$,$ F$\},\{$A$,$ C$\}->\{$M$,$ N$\},\{$D$,$ E$\}->\{$I$,$ J$,$ K$\},$

$\{$D$\}->\{$G$,$ H$\}\}.$

$($a$)(2\%)$ What is the key for R$?$

$($b$)(6\%)$ Decompose R into $2$NF$,$ then $3$NF relations