Let $p, q, r$ denote arbitrary statements. Then the logically equivalent of the statement $p\Rightarrow (q\vee r)$ 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

$\left(p^{\wedge} r\right) \Leftrightarrow\left(p^{\wedge}(\sim q)\right)$ is equivalent to $(\sim p)$ when $r$ is.

The false statement in the following is

The statement $(\sim( p \Leftrightarrow \sim q )) \wedge q$ is :

$(\sim (\sim p)) \wedge q$ is equal to .........