Set, Relation and FunctionEasy
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 ?
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
A.There is no rational number x ∈ S such that x ≤ 0
B.Every rational number x ∈ S satisfies x ≤ 0
C.x ∈ S and x ≤ 0 ⇒ x is not rational
D.There is a rational number x ∈ S such that x ≤ 0
Solution
P: there is a rational number x ∈ S such that x > 0
~P: Every rational number x ∈ S satisfies x ≤ 0
~P: Every rational number x ∈ S satisfies x ≤ 0
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