Consider the first-order logic sentence
ϕ=∃ s ∃ t ∃ u ∀ v ∀ w ∀ x ∀ y ψ(s, t, u, v, w, x, y)
where ψ (s t u v w x y , , , , , , ) is a quantifier-free-order logic formula using only predicate symbols and possibly equality, but no function symbols. Suppose φ has a model with a universe containing 7 elements.
Which one of the following statements is necessarily true?

Question

Examsnet · Accepted Answer

Correct Answer is : There exists no model of φ with universe of size less than or equal to 3.

GATE Computer Science (CS) 2018 Shift 1 Solved Paper