Let the operations $*, \odot \in\{\wedge, \vee\}$. If $( p * q ) \odot( p \odot \sim q )$ is a tautology, then the ordered pair $(*, \odot)$ is.

If $p \Rightarrow (\sim p \vee q)$ is false, the truth values of $p$ and $q$ are respectively

For any two statements $p$ and $q,$ the negation of the expression $p \vee ( \sim p\, \wedge \,q)$ is 

The conditional $(p \wedge q)  \Rightarrow  p$ is :-

Consider

Statement $-1 :$$\left( {p \wedge \sim q} \right) \wedge \left( { \sim p \wedge q} \right)$ is a fallacy.

Statement $-2 :$$(p \rightarrow q) \leftrightarrow ( \sim q \rightarrow   \sim  p )$  is a tautology.

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