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Problem 26: (Negating Quantifiers)

Rewrite each statement below using the quantifiers $\forall$ and/or $\exists$. Then write the negation of each statement.

  1. For each $x\in\mathbb{N}$ we have $x>4$.
  2. There exists $y\in \mathbb{R}$ such that $y\in (-3,4)$.
  3. For every $\varepsilon>0$, there exists a $\delta>0$ such that $0<|x-c|<\delta$ implies $\left|f(x)-L\right|<\varepsilon$.

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