Question

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

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

Answer 1

The correct option is B Every rational number $x\in S$ satisfies $x\le 0$

$P$: there is a rational number $x\in S$ such that $x>0$
$\sim P$: Every rational number $x\in S$ satisfies $x\le 0$
Hence, option 'B' is correct.