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

The contrapositive of $(p \vee q) \Rightarrow r$ is

$\sim p \wedge q$ is logically equivalent to

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

Given the following two statements :

$\left( S _{1}\right):( q \vee p ) \rightarrow( p \leftrightarrow \sim q )$ is a tautology.

$\left( S _{2}\right): \sim q \wedge(\sim p \leftrightarrow q )$ is a fallacy.

Then

The negative of the statement $\sim p \wedge(p \vee q)$ is