JEE MATHEMATICS MCQ: MATHEMATICAL REASONING

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Let

\mathrm{S}

be a non-empty subset of

\mathrm{R}

. Consider the following statement :

\mathrm{P}

: There is a rational number

x \in \mathrm{S}

such that

x>0

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

View answer and explanation

Correct option: B

Every rational number

x \in \mathrm{S}

satisfies

x \leq 0

Option B is correct. The negation of "there exists" is "for all", and the negation of x > 0 is x <= 0.

More Questions from MATHEMATICAL REASONING

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p:A

q:A

\sqrt{3}

p

q

p \rightarrow q

{F_1}(A,\,B,\,C) = \left( {A \wedge \sim B} \right) \vee \left[ { \sim C \wedge \left( {A \vee B} \right)} \right] \vee \sim A

{F_2}(A,\,B) = \left( {A \vee B} \right) \vee (B \to \, \sim \,A)

p

n

q:

n

p \Leftrightarrow q