The statement (p $$ \wedge $$ (p $$\to$$ q) $$\wedge$$ (q $$\to$$ r)) $$\to$$ r is :

Consider the two statements :

(S1) : (p $$\to$$ q) $$ \vee $$ ($$ \sim $$ q $$\to$$ p) is a tautology .

(S2) : (p $$ \wedge $$ $$ \sim $$ q) $$ \wedge $$ ($$\sim$$ p $$\wedge$$ q) is a fallacy.

Then :

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

Which of the following is the negation of the statement "for all M > 0, there exists x$$\in$$S such that x $$\ge$$ M" ?