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?

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x ∈ S and x ≤ 0⇒x is not rational.

There is a rational number x ∈ S such that x>0

There is no rational number x ∈ S such that x≤0

Every rational number x ∈ S satisfies x≤0

answer is D.

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Detailed Solution

P: there is a rational number x∈S such that x>0 ∼P: every rational number x∈S satisfies x≤0