The statement $\sim (p\leftrightarrow \sim q)$ is

1. equivalent to $p\leftrightarrow q$
2. a tautology
3. a fallacy
4. equivalent to $\sim p\leftrightarrow q$

The correct option is A equivalent to $p\leftrightarrow q$
$\begin{array}{cccccccc}p& q& \sim p& \sim q& p\leftrightarrow q& p\leftrightarrow \sim q& \sim p\leftrightarrow q& \sim (p\leftrightarrow \sim q)\\ T& F& F& T& F& T& T& F\\ F& T& T& F& F& T& T& F\\ T& T& F& F& T& F& F& T\\ F& F& T& T& T& F& F& T\end{array}$
Hence, $\sim (p\leftrightarrow \sim q)isequivalentto(p\leftrightarrow q)$.