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Suppose the relation R(A,B,C,D,E) is decomposed into R1(A,B,C), R2(A,D), and R3(A,C,E). Use the chase test to determine whether this decomposition is lossless, given each sets of FDs:

a, AC->B, C->D and A->E

b, A->B, AE->C and B->D

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