lossless and dependency preserving decomposition #testseries

Question

The below decomposition is lossless or lossy and also dependency preserving or not?

Comments

for lossy decomposition we check whether the final combination of table contain some spurious tuple or not.if yes then the decomposition will be lossy.

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Can anybody explain this by using chase algorithm?

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@night_fury

i don't know about that algorithm but i will give how to check is it lossy or loss less?

First take Table₁ ===> R₁(A,B,C)

list out all dependencies under this table by original FD set ==> { AB -> C }

Key of this table = AB

 

Table₂ ===> R₂(B,C,D)

list out all dependencies under this table by original FD set ==> { C -> D }

Key of this Table₂ = BC

 

Table₃ ===> R₃(C,D,E)

list out all dependencies under this table by original FD set ==> { C -> D }

Key of this Table₃ = CE

 

take the intersection of attributes of Table₁ and Table₂ ==> BC, it is a key(super key or primary key) in R2, therefore you can combine Table₁ and Table₂ . let denote it as T₁₂. it's key is AB

take the intersection of attributes of T₁₂ and Table₃ ==> CD, it is neither a key in T₁₂ nor R₁₃ ==> you can combine Table₁₂ and Table₃ . ===> it is lossy.

Answer 1

Lossy Decomposition because no common attribute is a candidate key here