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