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  1. \(\neg \exists x (E(x) \wedge O(x))\text{.}\)

  2. \(\forall x (E(x) \imp O(x+1))\text{.}\)

  3. \(\exists x(P(x) \wedge E(x))\) (where \(P(x)\) means “\(x\) is prime”).

  4. \(\forall x \forall y \exists z(x \lt z \lt y \vee y \lt z \lt x)\text{.}\)

  5. \(\forall x \neg \exists y (x \lt y \lt x+1)\text{.}\)

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