Question

Let R(A,B,C,D,E) be a relation with FDs F = {AB-CD, A-E, C-D, D-E} The decomposition of Rinto R1(A, B, C), R2(B, C, D) and R3(C, D, E) is 2 Points) Select one: Lossless and Dependency Preserving. Lossy and Not Dependency Preserving. Lossless and Not Dependency Preserving. Lossy and Dependency Preserving.

Answer 1

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Step 1 Let us first discuss about the concept

*** of Melation CR into sul relations not causes violation of Properties of Decomposition — Qcomposition any integrity it is easy less join decomposition (and) dependency preserving decomposition aprendency Prusuwung deomposition Rr with fD set (F) fi Ufa uf RI R2 () (FI) Because of the fact that decomposition should not lost anyth of fo

Loss less Jour decomposition JOIN mult of subrrelations must be equal to the Original relation. R Ra Ra RzER Ri Ra R3 into decomposed R1 R2 R3 Relation (R) is sul relations. ..R3 In general, [Ri - Rq as.... Rn ] 2 R NRN) = R, then it is lossless of Cri & Rz* join duomposition of (Rio Ra * -Rn) OR , it is called as lossy, join decomposition Here some extra tuples are generatid because of wrong decomposil.com, these are called spurious tuples.

with Notu- Relation R to set (f) decomposed into R1 R2 sub-relation given decomposition is lossless join decomposition iff 0 (RI UR) ER A wory abr of his in some sub RI Ronra is superkey for Ri Belaun of and (Ri NR) . Heus no ū 209 colour (or) Rin R2) •RQ IRIAR, is superkey for Ra wecause of and condition No spurious and Ý (RIA R2) =R * = {(RIURp=R) and (AN2 R, or R.net

# Dependency Preserving ducomposition - to set (f) decomposed into Relational Schuma R with with R1 R2 R3 fi fe fg ...fr Sub hulations Rn FO'S In general, Sri Ufa Uf3 U.. · En SF on is sf [Fi Urz. U.... in] =F, thin ducor decomposition Dependency preserving decomposition ( every to of his presenet of Chi UFQU ....fn] Cf, then decomposition is Not dependency preserving ducomposition. ✓ Here, because of decomposition, FD of f is cost. some FD
Step 2

Now come to the question

Given FDS F=Y AB->CD, A->E, C->D, D- og F = ABC, ABD, A-E,CD, DE) R RICA,BC) V 2CB,GDO V (>D R3CC,D, E) V AB->C PR-AB DE PK=BC PR=C R2 0 It is Lossless becallse RAR A R = RE RAR and R₂0 R3 R3 2 It is not dependency Preferring because AJE is not preserved So, option'c' is correct