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

Mathematics - Sets and Relations Question with Solution | TestHub

MathematicsSets and RelationsQuestions on Venn DiagramMedium2 minPYQ_2010

MathematicsMediumsingle choice

Let $S$ be a non-empty subset of R. Consider the following statement: $P$ : There is a rational number $x \in S$ such that $x > 0$ . Which of the following statements is the negation of the statement $P$ ?

Options:

Answer:

Solution:

$P$ : there is a rational number $x \in S$ such that $x > 0$ $\sim P$ : Every rational number $x \in S$ satisfies $x \leq 0$

Stream:JEESubject:MathematicsTopic:Sets and RelationsSubtopic:Questions on Venn Diagram

⏱ 2mℹ️ Source: PYQ_2010

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