Let S be a non-empty subset of R. Consider the following statement:p :

1.	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
Answer» Correct option: (C) Every rational number x ∈ S satisfies x ≤ 0 Given statement is ∃ x ∈ S, such that x > 0 ∴ ~ (∃ x ∈ S, such that x > 0) ≡ ∀ x ∈ S, x ≤ 0 i.e., Every rational number x ∈ S satisfies x ≤ 0.

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

Answer»

Correct option: (C) Every rational number x ∈ S satisfies x ≤ 0

Given statement is

∃ x ∈ S, such that x > 0

∴ ~ (∃ x ∈ S, such that x > 0)

≡ ∀ x ∈ S, x ≤ 0

i.e., Every rational number x ∈ S satisfies x ≤ 0.