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For each of the statements below, give a domain of discourse for which the statement is true, and a domain for which the statement is false.

  1. \(\forall x \exists y (y^2 = x)\text{.}\)

  2. \(\forall x \forall y (x \lt y \imp \exists z (x \lt z \lt y))\text{.}\)

  3. \(\exists x \forall y \forall z (y \lt z \imp y \le x \le z)\text{.}\)

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