Question

1. \forall x \in \mathbb{R}, \exists y \in \mathbb{R} \text{ such that } xy = 1. 2. \forall x, y \in \mathbb{R}, \exists n \in \mathbb{Z} \text{ such that } nx \ge y. 3. \forall x \in \mathbb{Z}, \exists y \in \mathbb{R} \text{ such that } \sqrt{x} = y. 4. \exists x \in \mathbb{R} \text{ such that } \forall y \in \mathbb{R}, xy = 0. 5. \forall x \in \mathbb{Q}, \exists n \in \mathbb{Z} \text{ such that } nx \in \mathbb{Z}. 6. \exists x \in \mathbb{R} \text{ such that } \forall y \in \mathbb{R}, xy = 1.

          1. \forall x \in \mathbb{R}, \exists y \in \mathbb{R} \text{ such that } xy = 1.
2. \forall x, y \in \mathbb{R}, \exists n \in \mathbb{Z} \text{ such that } nx \ge y.
3. \forall x \in \mathbb{Z}, \exists y \in \mathbb{R} \text{ such that } \sqrt{x} = y.
4. \exists x \in \mathbb{R} \text{ such that } \forall y \in \mathbb{R}, xy = 0.
5. \forall x \in \mathbb{Q}, \exists n \in \mathbb{Z} \text{ such that } nx \in \mathbb{Z}.
6. \exists x \in \mathbb{R} \text{ such that } \forall y \in \mathbb{R}, xy = 1.

1. ∀x ∈ℝ, ∃y ∈ℝ such that xy = 1.
2. ∀x, y ∈ℝ, ∃n ∈ℤ such that nx ≥y.
3. ∀x ∈ℤ, ∃y ∈ℝ such that √(x) = y.
4. ∃x ∈ℝ such that ∀y ∈ℝ, xy = 0.
5. ∀x ∈ℚ, ∃n ∈ℤ such that nx ∈ℤ.
6. ∃x ∈ℝ such that ∀y ∈ℝ, xy = 1.

Added by Zachary M.

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