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 $x \le 0$