$7.($a$)$ Consider the relation R$($A$,$ B$,$ C$,$ D$,$ E$)$ with the following functional dependencies:

A$->$ B$,$ AC$,$ CD $->$ E$,$ E $->$ D

Determine the closure of each functional dependency, find the candidate keys for $($R$)$

and identify the highest normal form of $($R$).$

$[5]$

$($b$)$ Given the relation R$($A$,$ B$,$ C$,$ D$,$ E$,$ F$)$ with the following functional dependencies:

A$->$B C$,$ CD$->$ E$,$ B$->$D$,$ E $->$ F

Identify all candidate keys, check for violations of the Second Normal Form $(2$NF$)$

and Third Normal Form $(3$NF$),$ and suggest necessary decompositions.

$[5]$