Let$$s suppose, a relation R $=($A$,$ B$,$ C$,$ D$,$ E$,$ F$)$ with a set of functional dependencies F: $($A $->$ B$,$ BC $->$ D$,$ EF $->$ A$,$ F $->$ E$)$ is given. Relation R is decomposed into R$1($A$,$ B$,$ C$,$ D$)$ and R$2($A$,$ E$,$ F$).$ Find out whether the decomposition is lossless or not, and whether it is dependency preserving or not $($show why or why not$).$