Checkout JEE MAINS 2022 Question Paper Analysis : Checkout JEE MAINS 2022 Question Paper Analysis :

If 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 statement P?

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 statement P?

1) There is a rational number x ∈ S such that x ≤ 0

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

3) Every rational number x ∈ S satisfies x ≤ 0

4) x ∈ S and x ≤ 0 ⇒ x is not rational

Solution: (3) Every rational number x ∈ S satisfies x ≤ 0

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

~ P: Every rational number x ∈ S satisfies x ≤ 0.

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