Q. 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 $x \leq 0$
B) There is no rational number $x \in S$ such that $x \leq 0$
C) Every rational number $x \in S$ satisfies $x \leq 0$
D) $x \in S$ and $x \leq 0 \Rightarrow x$ is not rational
Explanation
(c)
$P\ :$ There is rational number $x \in S$ such that $x > 0$
$\sim P\ :$ Every rational number $x\ \in S$ satisfies $x \leq 0$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.