Part $1$: Functional Dependencies $(40\%)$

NOTES: Underlined attributes are either the primary key or part of the primary key. Fo example, $R(A_{,}{B}_{,}C)$ indicates that $A,B$ is a composite primary key.

Use the same notation as in the text.

For example, to take the following relation: $R(x,Y,Z)$ with $FD$:$(x,Y)Z$ and $(x,Z)Yf$ to $BCNF,$ you would recommend the following: $R(x,Z)$ and $R2(Z_{,}Y),$ as described in the page $167$ using the STUDENT$\_$ADVISOR relation.

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

$(A,B)C$

$(A,B)D$

$DE$

a$.$ What normal form does this relation violate?

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