Question

Which of the following tuple relational calculus expression(s) is/are equivalent to ∀t ∈ r(P(t))?

I. ¬∃t ∈ r(P(t))
II. ∃t ∉ r(P(t))
III. ¬∃t ∈ r(¬P(t))
IV. ∃t ∉ r(¬P(t))

Accepted Answer

The correct answer is (C) III only. ∀t∈r P(t) is logically equivalent to ¬∃t∈r ¬P(t) — the standard universal-to-existential conversion (III). I negates P(t) itself inside the existential rather than negating the whole quantified statement — wrong. II and IV talk about tuples OUTSIDE r, which is entirely unrelated to a statement about tuples IN r. Only III is equivalent.

Explanation