Consider the schema with the attribute set ABCDEFH and the FDs. Prove that the decomposition (AD; A ? D ), (CE; C ? E ), (FA ; F ? A), (EF ; E ? F ), (BHE; BH ? E) is not lossless by providing a concrete relation instance over ABCDEFH that exhibits the loss of information when projected on this schema.
What will be an ideal response?
This relation satis?es all the FDs. It is easy to verify, however, that the tuple a a a a a a a belongs to the join of the projections of this relation on the above schemas, but it is not one of the tuples in this relation. Therefore, this relation exhibits a case where information loss occurs due to the decomposition.
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