Lossy Join In database

Question

Consider a schema R (A, B, C, D, E, F) and functional dependencies are A → B, C → D, B → E Which is divided into R, (A, B, E), R2 (C, D, E) then decomposition?

(1)	Dependency preserving and loss Join
(2)	Loss less join but not dependency preserving
(3)	Dependency preserving but not loss join
(4)	Not dependency preserving and not loss Join

Answer 1

F={A->B,C->D,B->E}

Lossless Join:

R1(ABE) AND R2(CDE)

(R1 $\bigcap$ R2)^+=R1 OR R2 Then it is lossless join dependecy.

R1 $\cap$ R2=$E^{+}$ which is not R1 or R2.

Hence it is lossy join dependency.

Dependency preserving:

R1(ABE) ---A->BE,B->E,AB->E

R2(CDE)---C->D.

R={A->BE,B->E,AB->E,C->D}

F=R .

Hence it is dependecy preserving.

Hence it is lossy join and dependecy preserving.Option '3' is correct.

Comments

i think it is lossy , because the common Field "E" is not primary key in any of the decomposed table.

Correct me...

so it should be lossy and it is obviously dependency preserving.

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i am also saying it is lossy join.

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so option 1 should be right?? but you said option 3 is right.

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it is dependecy preserving and not lossless join.so option 3 is correct.