Consider the first-order logic sentence where

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Computer Science & IT

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Consider the first-order logic sentence

where 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?

[GATE CS 2018]

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 of size greater than 7.

D Every model of φ has a universe of size equal to 7.