2. Consider the followingrelation E(C, S, T, R, G) with the followingconditions:

Question

2.        Consider the followingrelation E(C, S, T, R, G) with the followingconditions: CàT, STàR, TRàC,SCàG

a)       Is the decompositiondependency preserving? Justify your answer.

Explanation / Answer

suppose R is decomposed into X, Y, Z...with functional dependenciesf1, f2,f3... now The decomposition is said to be dependency preserving if allthe functional dependencies of R can be derived from F1, F2,F3; Here the relation is E(C,S,T,R,G) and its functional dependencies are F= { C->T, ST ->R ,TR->C,SC->G} now decompose E to X(C,T) and F1= {C->T}                                 Y(S, C, R, G) AND F2={SC->G, SC->R}                                 Z(T, R, C) and F3={TR -> C} now from F1, F2, F3 we can derive {C->T, SC->G,TR->C} very easily. for the fourth dependency....SC->R and C->T soST->R..since T is functionally depends on C...so C can derivet Therefore ST->R Therefore all the functional dependencies of E can be derived fromthe above decomposition.. so decomposition of E into X, Y, Z is a dependency preservingdecomposition

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