Practicing Success

Target Exam

CUET

Subject

-- Mathematics - Section B1

Chapter

Relations and Functions

Question:

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?

Options:

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

Every rational number x ∈ S satisfies x ≥ 0

x ∈ S and x ≤ 0 ⇒ x is not rational

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

Correct Answer:

Every rational number x ∈ S satisfies x ≥ 0

Explanation:

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

∼ P : Every rational number x ∈ S satisfies x ≤ 0