Dependency-Preserving decomposition (Theory)

Hey,
Just running through some practice papers for a database exam and I'm stuck on dependancy preserving decomposition

Code:

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Relation T defined over attributes A,B,C,D,E
Functional Dependancies:
B->E
E->A
A->D
D->E

Determine if decomposition of T into AB, BCD, ADE will be dependency preserving

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Could anyone show me how to work this out?

Thanks for any help.

To check wheather this decompostion will preseve the dependency simply calcuate the closurse union of these three decomposed relations, see if it logically implies the original FDs.

What I mean by that is
R1(A,B), R2(BCD) and,R3( ADE)

(R1 UNION R2 UNION R3 UNION) + = F+

(ABCDE)+ =F+

ABCDE supports all the originally dependency. So this decomposition preseves the dependency