$\sim (p \vee q)$ is equal to

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 logically equivalent to $\sim(\sim p \Rightarrow q)$

If the truth value of the Boolean expression $((\mathrm{p} \vee \mathrm{q}) \wedge(\mathrm{q} \rightarrow \mathrm{r}) \wedge(\sim \mathrm{r})) \rightarrow(\mathrm{p} \wedge \mathrm{q}) \quad$ is false then the truth values of the statements $\mathrm{p}, \mathrm{q}, \mathrm{r}$ respectively can be:

Which of the following statement is a tautology?

If $P \Rightarrow \left( {q \vee r} \right)$ is false, then the truth values of $p, q, r$ are respectively