Solve this: 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. $.$

Example:

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a$)[10$ points$]$ Let $R(A,B,C,D,E,F)$ be a relation schema, and let $A,CFD,EFB,CE$ be a set of functional dependencies. Use the Chase test to determine if the following decomposition is lossless.

Decomposed relations: $R_1(A,B,E),R_2(B,D,E),R_3(C,E,F),R_4(C,D,F)$

Solution:

$\backslash$table$[[$Initial tableau,A$,$B$,$C$,$D$,$E$,$F$],[$ABE$,a,b,c_1,d_1,e,f_1$