\(\neg \exists x (E(x) \wedge O(x))\text{.}\)
\(\forall x (E(x) \imp O(x+1))\text{.}\)
\(\exists x(P(x) \wedge E(x))\) (where \(P(x)\) means “\(x\) is prime”).
\(\forall x \forall y \exists z(x \lt z \lt y \vee y \lt z \lt x)\text{.}\)
\(\forall x \neg \exists y (x \lt y \lt x+1)\text{.}\)