Which of the following is the negation of the statement "for all $M\,>\,0$, there exists $x \in S$ such that $\mathrm{x} \geq \mathrm{M}^{\prime \prime} ?$
Which of the following is the negation of the statement "for all $M\,>\,0$, there exists $x \in S$ such that $\mathrm{x} \geq \mathrm{M}^{\prime \prime} ?$
- [JEE MAIN 2021]
- A
there exists $M\,>\,0$, such that $x \geq M$ for all $x \in S$
- B
there exists $M\,>\,0$, there exists $x \in S$ such that $x \geq M$
- C
there exists $M\,>\,0$, such that $x < M$ for all $x \in S$
- D
there exists $M\,>\,0$, there exists $x \in S$ such that $x < M $
Similar Questions
Which of the following statement is a tautology?
Which of the following statement is a tautology?
The negation of the statement $''96$ is divisible by $2$ and $3''$ is
The negation of the statement $''96$ is divisible by $2$ and $3''$ is
The Boolean Expression $\left( {p\;\wedge \sim q} \right)\;\;\vee \;q\;\;\vee \left( { \sim p\wedge q} \right)$ is equivalent to:
The Boolean Expression $\left( {p\;\wedge \sim q} \right)\;\;\vee \;q\;\;\vee \left( { \sim p\wedge q} \right)$ is equivalent to:
- [JEE MAIN 2016]
Which of the following is equivalent to the Boolean expression $\mathrm{p} \wedge \sim \mathrm{q}$ ?
Which of the following is equivalent to the Boolean expression $\mathrm{p} \wedge \sim \mathrm{q}$ ?
- [JEE MAIN 2021]
The statement $B \Rightarrow((\sim A ) \vee B )$ is equivalent to
The statement $B \Rightarrow((\sim A ) \vee B )$ is equivalent to
- [JEE MAIN 2023]