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 $x>0$. The negation of $p$ is

• 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 $x\in S$ such that $x\le 0$
  
• D. $x\in S$ and $x\le 0\Rightarrow x$ is not rational

Answer 1

The correct option is C Every rational number $x\in S$ such that $x\le 0$


$p:\exists$ a rational number $x\in S;x>0$
$\sim p:\forall$ rational numbers $x\in S;x\le 0$