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 ?

Correct answer: B. 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

JEE Main 2010

Exam: JEE Main
Year: 2010
Subject: Mathematics
Chapter: Sets and Relations

JEE Main 2010 · Mathematics · Sets and Relations

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

Let

S

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

\mathrm{P}

: There is a rational number

\mathrm{x} \in \mathrm{S}

such that

\mathrm{x}>0

. Which of the following statements is the negation of the statement

P

Options

AThere is no rational number $x \in S$ such that $x \leq 0$
BEvery rational number $x \in S$ satisfies $x \leq 0$
C $x \in S$ and $x \leq 0 \Rightarrow x$ is not rational
DThere is a rational number $x \in S$ such that $x \leq 0$

Correct answer

B. Every rational number $x \in S$ satisfies $x \leq 0$

Step-by-step solution

P

: there is a rational number

x \in S

such that

x>0

\sim P

: Every rational number

\mathrm{x} \in \mathrm{S}

satisfies

\mathrm{x} \leq 0

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