Which of the following relational calculus expressions is not safe?
2001
Which of the following relational calculus expressions is not safe?
- A.
{t | ∃u ∈ R1 (t[A] = u[A]) ∧ ¬∃s ∈ R2 (t[A] = s[A])}
- B.
{t | ∀u ∈ R1 (u[A] = "x" ⇒ ∃s ∈ R2 (t[A] = s[A] ∧ s[A] = u[A]))}
- C.
{t | ¬(t ∈ R1)}
- D.
{t | ∃u ∈ R1 (t[A] = u[A]) ∧ ∃s ∈ R2 (t[A] = s[A])}
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Correct answer: C
A relational calculus expression is safe only when its result is restricted to values from the active database domain, so it cannot generate an infinite set of arbitrary tuples.
Option C is {t | ¬(t ∈ R1)}. This asks for all tuples t that are not in R1. Since t is not positively range-restricted by any relation or finite domain, the result can include infinitely many tuples outside the database. Therefore, option C is not safe.
The other expressions range-restrict t through equality with values coming from R1 and/or R2, so their results are bounded by database values. Hence, option C is correct.