Consider a relation R$($ABCDEFGHIJ$)$ with the following set of functional dependencies

G $=\{$ F $$ AB$,$ CD $$ E$,$ C $$ FG$,$ H $$ IJ$,$ D $$ H $\}$

$1.$ Is CDE a superkey of R $($w$.$r$.$t$.$ G$)?$

$2.$ Is CDE a key of R $($w$.$r$.$t$.$ G$)?$

$3.$ Apply the appropriate algorithm to determine a key for R $($w$.$r$.$t$.$ G$).$

$4.$ Apply the appropriate algorithm to determine all the keys for R $($w$.$r$.$t$.$ G$).$

$5.$ Determine the prime attributes of R$.$

$6.$ Is R in BCNF $($w$.$r$.$t$.$ G$)?$

$7.$ Is R in $3$NF $($w$.$r$.$t$.$ G$)?$

$8.$ Determine whether the decomposition D $=\{$ CDE, CFG$,$ DH$,$ HIJ, FAB $\}$ has $($i$)$ the dependency

preservation property and $($ii$)$ the lossless join property, with respect to G$.$ Also determine which normal

form each relation in the decomposition is in$.$