CSE 233 Spring, 2012
Problem Set #2
Due on Tuesday, May 1
This is an individual assignment and the usual criteria for academic
integrity apply. It is recommended to typeset your answer (latex preferred).
1. Let q1, q2, q3be conjunctive queries (no equality). Prove that, if q1⊆
(q2∪q3), then q1⊆q2or q1⊆q3(recall that the notation p⊆rfor queries
p, r means that p(I)⊆r(I) for every database I).
2. Let Rbe a relation with attributes ABC D. Consider the algebra query
πAC [πAB(R)1πB C (σC=0(R))] 1πC D(σB=5(R)).
(a) Construct the tableau corresponding to the query. Is it minimal (ex-
plain)?
(b) Using the chase, minimize the tableau in (a) knowing that the query
is only applied to databases satisfying the FDs
A→D, CD →B , C →A.
(c) Construct an algebra query corresponding to the minimized tableau
obtained in (b).
3. Let Rbe a relation over ABCD E. Minimize the number of joins in the
query
πACE (R)1πADE (R)1πB CD(R)
knowing that it is only applied to relations Rsatisfying the set of constraints
{A→B, E →D, D →→ E}.
4. Prove or disprove the following statement: it is possible for a set of
MVDs to imply a non-trivial FD. More precisely, there exists a set ∆ of
MVDs and a non-trivial FD fsuch that ∆ |=f. (An FD is trivial if it is of
the form X→Ywhere Y⊆X; such an FD is always true.).
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