Q. 54 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 first-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?
(A) There exists at least one model of φ with universe of size less than or equal to 3
(B) There exists no model of φ with universe of size less than or equal to 3
(C) There exists no model of φ with universe size of greater than 7
(D) Every model of φ has a universe of size equal to 7
Answer: (A)
Explanation:
