Suppose you are given a relation $R=\{A_{,}B,C,D\}.$ Further, the following Functional

Dependencies that hold on $R$ are $F=\{AB,BCD,AC,AD\}.$

a$.$ Identify the highest normal form that $R$ satisfies $(1$NF$,2$NF$,3$NF$,$ and BCNF$).$ Explain your answer.

b$.$ If $R$ is not in $BCNF,$ decompose it into a set of $BCNF$ relations.