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Problem 25: (The Order Of Quantifiers Matters)

Translate each of the following into an English sentence. Then determine the truth value of each statement.

  1. $\forall x \in \mathbb{R}, \exists y\in\mathbb{R}$ such that $y+1>x$.
  2. $\exists y \in \mathbb{R}$ such that $\forall x \in \mathbb{R}$, we have $y+1>x$.

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