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

Let TV of (r) denotes truth value of a statement r.

$\begin{array}{l} \text { Now, if } T V(p)=T V(q)=T \\ \Rightarrow T V\left(S_{1}\right)=F \\ \text { Also, if } T V(p)=T \& T V(q)=F \\ \Rightarrow T V\left(S_{2}\right)=T \end{array}$

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