Given that S is a non-empty subset of R. - P : There is a rational number x∈S such that x>0. Now, we need to find the negation of P. Clearly, P is equivalent to saying that "There is a positive rational number in S. So, its negation (∼P) is "There is no positive rational number in S ". Thus, for ∼P : There exists no positive rational number in S. - ⇔∼P : Every rational number x∈S satisfies x≤0.