3.7

Consider the SQL query

SELECT p.a1
FROM p, r1, r2
WHERE p.a1 = r1.a1 OR p.a1 = r2.a1

Under what conditions does the preceding query select values of p.a1 that are either in r1 or in r2 ? Examine carefully the cases where either r1 or r2 may be empty.

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The query selects those values of p.a1 that are equal to some value of r1.a1 or r2.a1 if and only if both r1 and r2 are non-empty. If one or both of r1 and r2 are empty, the Cartesian product of p, r1 and r2 is empty, hence the result of the query is empty. If p itself is empty, the result is empty.