Question

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 $P$ ?

• A. There is a rational number $x\in S$ such that $x\le 0$
• B. There is no rational number $x\in S$ such that $x\le 0$
• C. Every rational number $x\in S$ satisfies $x\le 0$
• D. $x\in S$ and $x\le 0\Rightarrow x$ is not rational

Answer 1

Answer: (C)

$P:$ There is rational number $x\in S$ such that $x>0$
$\sim P$ : Every rational number $x\in S$ satisfies $x\le 0$