Negation of a statement with 'for all' or 'there exists'

1. A.
   There is a rational number $x \in S$ such that $x \leq 0$
2. B.
   There is no rational number $x \in S$ such that $x \leq 0$
3. C.
   Every rational number $x \in S$ satisfies $x \leq 0$
4. D.
   $x \in S$ and $x \leq 0 \Rightarrow x$ is not a rational number

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1. A.
   $\ \exists M > 0$ such that $x \geqslant M$ for all $x \in S$
2. B.
   $\exists M > 0,\exists x \in \text{ }s$ such that $x \geqslant M$
3. C.
   $\exists M > 0$ such that $x < M$ for all $x \in S$
4. D.
   $\exists M > 0$, there exist $x \in \text{ }s$ such that $x < M$

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