Consider a relation on attributes ABCDEF and the FDs {EF → AD, C → F, AC → DE, F → BD}. Compute a minimal basis for this set of functional dependencies. If it is already a minimal basis, write "already an MB. Include your rough work and show the steps of the minimal basis algorithm.

Here's a relation (R), its attributes and its functional dependencies (F): R(A, B, C, D, E, F, G) BC -> DG CD -> F FG -> A   1. compute the closure of {ACD}+ 2. compute the closure of {F}+ 3. what are the keys of R?

Consider the relation schema R=VWXYZ, with the set of functional dependencies F = {VW->XY, V>X, W->Z, YZ->Z, Z→V} A. Give three independent reasons why the following table cannot possibly be a legal instance of R. V W X Y v1 w1 х1 yl z1 v2 w1 x2 y2 z1 v2 w2 x1 y2 z2 B. Show the functional dependencies that hold on each of R1=VWX and R2=WYZ. You do not need to show trivial functional dependencies, or those implied by others in the same set, but you must show all others. C. Is the decomposition of R into R1=VWX and R2=WYZ lossless-join? Why or why not?

Let's suppose, a relation R=(A, B, C, D, E. H) with a set of functional dependencies F: (AE->BC, B ->AD, CD->E, E→CD, A->E) is given. Relation R (A, B, C, D, E, H) is decomposed into R1 (A, B, C, D) and R2 (A, B, E, H). Find out whether the decomposition is lossless or not, and whether it is dependency preserving or not.