Let S be a non-empty subset of R. Consider the following statement:
P : There is a rational number x ∈ S such that x > 0.
Which of the following statements is the negation of the statement P ?
(a) There is a rational number x ∈ S such that x ≤ 0.
(b) There is no rational number x ∈ S such that x ≤ 0
(c) Every rational number x ∈ S satisfies x ≤ 0.
(d) x ∈ S and x ≤ 0 ⇒ x is not rational.