If $q$ is false and $p\, \wedge \,q\, \leftrightarrow \,r$ is true, then which one of the following statements is a tautology?

Among the statements:

$(S1)$ $\quad(( p \vee q ) \Rightarrow r ) \Leftrightarrow( p \Rightarrow r )$

$(S2) \quad(( p \vee q ) \Rightarrow r ) \Leftrightarrow(( p \Rightarrow r ) \vee( q \Rightarrow r ))$

If $p : 5$ is not greater than $2$ and $q$ : Jaipur is capital of Rajasthan, are two statements. Then negation of statement $p \Rightarrow  q$ is the statement

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

Let $p$ and $q$ denote the following statements
$p$ : The sun is shining
$q$ : I shall play tennis in the afternoon

The negation of the statement "If the sun is shining then I shall play tennis in the afternoon", is 

The Boolean expression $(\mathrm{p} \wedge \mathrm{q}) \Rightarrow((\mathrm{r} \wedge \mathrm{q}) \wedge \mathrm{p})$ is equivalent to :