The statement $( p \rightarrow( q \rightarrow p )) \rightarrow( p \rightarrow( p \vee q ))$ is

Among the two statements

$(S1):$ $( p \Rightarrow q ) \wedge( q \wedge(\sim q ))$ is a contradiction and

$( S 2):( p \wedge q ) \vee((\sim p ) \wedge q ) \vee$

$( p \wedge(\sim q )) \vee((\sim p ) \wedge(\sim q ))$ is a tautology

The negation of $ \sim s \vee \left( { \sim r \wedge s} \right)$ is equivalent to

The negation of the statement $q \wedge \left( { \sim p \vee  \sim r} \right)$

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

Which of the following is the negation of the statement "for all $M\,>\,0$, there exists $x \in S$ such that $\mathrm{x} \geq \mathrm{M}^{\prime \prime} ?$