JUNE 2012 - PAPER III

18. Consider a schema R(A, B, C, D) and functional dependencies A → B and C → D. Then the decomposition R1(A, B) and R2(C, D) is
(A) Dependency preserving but not lossless join
(B) Dependency preserving and lossless join
(C) Lossless Join but not dependency preserving
(D) Lossless Join

Ans:-A

Explanation:-
I have given the explanation in question no. 17 of December 2010 UGC paper. I am repeating it once again here for dependency preservation and lossless join. First of all let us consider the dependency preservation and how to understand it.
Definition of Dependency preservation decomposition:-

Each FD specified in F either appears directly in one of the relations in the decomposition, or be inferred from FDs that appear in some relation.


Let us consider the above example for Dependency preservation



Let R be a relation R(A B C D)

Let there be 2 functional dependencies.

FD1: A->B

FD2: C->D


Let the relation R be decomposed into two more relations.

R1(A B )  :  R2(C D)

Let us first consider the relation R1(A B ). Here between A and B the functional dependency FD1 is preserved.

Let us now consider the second relation R2(C D). Between C and D the FD, FD2 is preserved. So in the two relations R1 and R2, all the 2 functional dependencies are preserved.

Now for the lossless join.
A decomposition of R into R1 and R2 is lossless join if and only if at least one of the following dependencies is in F*: R1 ∩ R2 -> R1 R1 ∩ R2 -> R2 In the above example, R1 ∩ R2 = { null }. So, it is not a lossless join. So the answer is dependency preserving but not lossless join. So, the answer is option A.

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19. The quantiser in an image-compression system is a
(A) lossy element which exploits the psychovisual redundancy
(B) lossless element which exploits the psychovisual redundancy
(C) lossy element which exploits the statistical redundancy
(D) lossless element which exploits the statistical redundancy

Ans:-A

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20. Data Warehouse provides
(A) Transaction Responsiveness
(B) Storage, Functionality Responsiveness to queries
© Demand and supply Responsiveness
(D) None of the above

Ans:-B

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