In TRC, which of the following mathematical notations is used as a quantifier…
2024
In TRC, which of the following mathematical notations is used as a quantifier to express that at least one tuple in the relation satisfies a specific condition?
- A.
∀
- B.
∃
- C.
σ
- D.
π
- E.
∪
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Correct answer: B
Tuple Relational Calculus (TRC) is a non-procedural query language in which queries are written as {t | P(t)}, where t is a tuple variable and P(t) is a logical predicate. To state a condition over tuples, TRC uses two quantifiers borrowed from predicate logic:
the existential quantifier ∃ (“there exists” / “there is at least one”), and the universal quantifier ∀ (“for all” / “for every”).
The phrase “at least one tuple in the relation satisfies a condition” is exactly the meaning of the existential quantifier: ∃t (R(t) ∧ condition) is true when one or more tuples make the condition true. Hence the correct notation is ∃ (option 2).
The other symbols are not quantifiers: ∀ expresses “for all tuples” (a universal claim, not “at least one”), while σ (selection), π (projection) and ∪ (union) are operators of relational algebra, not quantifiers of relational calculus.