Consider a relation schema $R=(A,B,C,D,E)$ with the set of functional dependencies $F=$

$\{ABC,CDE,BD,EA\}.$

$($a$)$ Compute the closure of F$?$

$($b$)$ If we decompose the relation $R$ into R$1(A,B,C$ and $R2(A,D,E)$ then show this

decomposition is a lossless decomposition.