Given the following two statements:\\
$\left( \mathrm { S } _ { 1 } \right) : ( \mathrm { q } \vee \mathrm { p } ) \rightarrow ( \mathrm { p } \leftrightarrow \sim \mathrm { q } )$ is a tautology\\
$\left( \mathrm { S } _ { 2 } \right) : \sim \mathrm { q } \wedge ( \sim \mathrm { p } \leftrightarrow \mathrm { q } )$ is a fallacy. Then :\\
(1) both ( $S _ { 1 }$ ) and ( $S _ { 2 }$ ) are not correct.\\
(2) only ( $S _ { 1 }$ ) is correct.\\
(3) only ( $S _ { 2 }$ ) is correct.\\
(4) both $\left( S _ { 1 } \right)$ and $\left( S _ { 2 } \right)$ are correct.