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
The number of ordered triplets of the truth values of $p, q$ and $r$ such that the truth value of the statement $(p \vee q) \wedge(p \vee r) \Rightarrow(q \vee r)$ is True, is equal to
The number of ordered triplets of the truth values of $p, q$ and $r$ such that the truth value of the statement $(p \vee q) \wedge(p \vee r) \Rightarrow(q \vee r)$ is True, is equal to
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When does the current flow through the following circuit
When does the current flow through the following circuit
The Boolean expression $(p \wedge \sim q) \Rightarrow(q \vee \sim p)$ is equivalent to:
The Boolean expression $(p \wedge \sim q) \Rightarrow(q \vee \sim p)$ is equivalent to:
- [JEE MAIN 2021]
Statement$-I :$ $\sim (p\leftrightarrow q)$ is equivalent to $(p\wedge \sim q)\vee \sim (p\vee \sim q) .$
Statement$-II :$ $p\rightarrow (p\rightarrow q)$ is a tautology.
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Statement$-II :$ $p\rightarrow (p\rightarrow q)$ is a tautology.
Let $p , q , r$ be three statements such that the truth value of $( p \wedge q ) \rightarrow(\sim q \vee r )$ is $F$. Then the truth values of $p , q , r$ are respectively
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- [JEE MAIN 2020]