Suppose that we decompose the schema R$=($A$,$B$,$C$,$D$,$E$)$ into

$($A$,$B$,$C$)($C$,$D$,$E$),$

Determine whether this decomposition is a lossless decomposition if the following set F of functional dependencies holds :

A$->$ BC

C$->$ DE

B$->$ D

E$->$ A