$16.$ Let R$($A$,$ B$,$ C$,$ D$,$ E$,$ F$)$ be a relation schema, and let S $=\{$A $->$ B$,$ AB $->$ C$,$ AC $->$ E$,$ B $->$ CF$,$ BC $->$ DE$\}$ be a set of functional dependencies. Use the Chase test to determine if the decomposition of R into the relation schemas R$($A$,$ B$,$ E$),$ R$($A$,$ D$),$ R$($B$,$ D$,$ E$),$ and R$($B$,$ C$,$ F$)$ is lossless.

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