Exercise 3.48. Disprove each of the following statements.
(1) \exists x \in \mathbb{R}, \exists y \in \mathbb{R}, x^2 = -y^2 - 1.
(2) \forall x \in \mathbb{R}, \exists y \in \mathbb{R}, x \ge y^2 - 100.
(3) \exists x \in \mathbb{R}, \forall y \in \mathbb{R}, x^2 \le y + 100.
(4) \forall x \in \mathbb{R}, \forall y \in \mathbb{R}, x^2 > -y^2.