Given the following two statements:

$$\left( {{S_1}} \right):\left( {q \vee p} \right) \to \left( {p \leftrightarrow \sim q} \right)$$ is a tautology

$$\left( {{S_2}} \right): \,\,\sim q \wedge \left( { \sim p \leftrightarrow q} \right)$$ is a fallacy. Then:

Let p, q, r be three statements such that the truth value of
(p $$ \wedge $$ q) $$ \to $$ ($$ \sim $$q $$ \vee $$ r) is F. Then the truth values of p, q, r are respectively :

The proposition p $$ \to $$ ~ (p $$ \wedge $$ ~q) is equivalent to :

Which of the following is a tautology ?