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Let $S$ be a non-empty subset of $R .$ Consider the following statement :
$P:$ There is a rational number $x \in S$. such that $x>0$ Which of the following statements is the negation of the statement $P$ ?

1) There is no rational number $x \in S$ such that $x \leq 0$
2) Every rational number $x \in S$ satisfies $x \geq 0$
3) $x \in S$ and $x \leq 0 \Rightarrow x$ is not rational
4) There is a rational number $x \in S$ such that $x \leq 0$
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(4)

Explanation

$\mathrm{P}:$ there is a rational number $x \in S$ such that $x>0$
$\sim P:$ Every rational number $x \in S$ satisfies $x \leq 0$

by Diamond (75,948 points)

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