Let $S$ be a non empty subset of $R$. Consider the following statement: $P$: There is a rational number $x \in S$ such that $x\gt 0$. Then, which of the following statements is the negation of statement $P$:

Question

$\begin{array}{1 1}(A) x \in \; and x \leq 0 \Rightarrow \text{x is not rational} \\ (B) \text{Every rational number} x \in \; satisfies\; x \leq 0 \\(C) \text{There is no rational number} x \in such that x \leq 0 \\(D) \text{There is a rational number} x \in such\; that \;x \leq 0 \end{array}$