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SQL Transactions Exercises For the universal relation R(w,x,y,z), consider the d

ID: 3841998 • Letter: S

Question

SQL Transactions Exercises

For the universal relation R(w,x,y,z), consider the decomposition D consisting of R1(w,y,z) and R2(x,y), and the set F of functional dependencies { y->xz ; yz->w ; x->w }.

Recall that the projection of set of functional dependences G on relation Rx consists of every functional dependency in (G)+ that contains only attributes from Rx.

a. Compute the projection of F on R1.

b. Compute the projection of F on R2.

c. Does the decomposition D preserve the set of dependencies F? Why or why not?

Explanation / Answer

Given set of functional dependencies
F = {y->x, y->z, yz->w, x->w}

a. projection of F on R1(w,y,z) must contain FDs with attributes w, y, z only.
F1 = {y->z, yz->w}

b. projection of F on R2(x, y) must contain FDs with attributes x, y only
F2 = {y->x}

c. The decomposition doesn't preserve dependencies because the FD, x->w is nethier present in F1 nor in F2. It has never been projected onto the decomposed relations.