Q35

Consider the first order predicate formula $\varphi$: $\forall x [ ( \forall z \: z | x \Rightarrow (( z=x) \vee (z=1))) \rightarrow \exists w ( w > x) \wedge (\forall z \: z | w \Rightarrow ((w=z) \vee (z=1)))]$ Here $a \mid b$ denotes that $’a \text { divides } b’$ , where $a$ and $b$ are integers. Consider the following sets: $S_1: \{1, 2, 3, \dots , 100\}$ $S_2:$ Set of all positive integers $S_3:$ Set of all integers Which of the above sets satisfy $\varphi$?