$1.$ Given that relation $($R$)$ has the following structure: R$($A$,$ B$,$ C$,$ D$,$ E$)$ with functional dependencies:

$($A$,$B$)->$ C

$($A$,$B$)->$ D

$$ D $->$ E

a$.$ What is the lowest normal form that this relation violates? $($Lowest normal form is $1$st$,$ followed by $2$nd$,$ followed by $3$rd$,$ followed by Boyce$-$Codd Normal Form. If a relation, has a partial dependency, then it satisfies $1$st normal form but violates $2$nd normal form.$)$

b$.$ Using the relational notation format above, modify the relation so that it is in Boyce$-$Codd Normal Form $($BCNF$).$