Fall 2009 CS127 Homework #4 Due October 26, 2009
Problem 1
Suppose you are given a relation R(A, B, C, D). For each of the following sets
of FD’s that hold over R, do the following:
(i) Suggest a candidate key for R.
(ii) Suggest a normalization to BCNF, and whether or not it is Dependency
Preserving.
1.{A→B, B →C, A →D}.
2.{BC →A, D →A}.
3.{B→C, D →A, AC →D}.
Problem 2
Suppose we have a relation R(A, B, Y, V ) and the set of FD’s F={B→
Y, V A →Y, Y A →V, B Y →V}. Note that when calculating closures of in the
problems that follow, you don’t need to include trivial functional dependencies.
(i) Calculate F+.
(ii) Calculate B+.
(iii) Calculate a canonical cover for R.
Problem 3
Given the following relation R(A, B, C, D, E, F ) and the set of FD’s {A→
CD, C B →E , F →A}state whether the following decomp ositions. . .
(i) . . . are Dependency Preserving
(ii) . . . allow Lossless Joins
1.F AC and CB DE.
2.F ACD and C BE.
3.F ACB and C DEF .
Problem 4
Give informal arguments, using the definition of functional dependencies, that
each of Armstrong’s Axioms are true.
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