Consider the first order predicate formula 𝜑: ∀𝑥 [(∀𝑧 𝑧|𝑥 ⇒ ((𝑧 = 𝑥) ∨…

Consider the first order predicate formula 𝜑:

∀𝑥 [(∀𝑧 𝑧|𝑥 ⇒ ((𝑧 = 𝑥) ∨ (𝑧 = 1))) ⇒ ∃𝑤 (𝑤 > 𝑥) ∧ (∀𝑧 𝑧|𝑤 ⇒ ((𝑤 = 𝑧) ∨ (𝑧 = 1)))]

Here ‘a|b’ denotes that ‘a divides b’, where a and b are integers. In this question, count only positive divisors a; x, z, and w range over the stated set.

S1. {1,2,3, … , 100}

S2. Set of all positive integers

S3. Set of all integers

Which of the above sets satisfy 𝜑?