JEE Main · 2014 · 06 Apr 2014 · Offline · Mathematical Reasoning *

Look at when $\sim (p\leftrightarrow \sim q)$ is true. The biconditional $p\leftrightarrow \sim q$ holds when $p$ and $\sim q$ carry the same truth value, so its negation is true exactly when $p$ and $\sim q$ differ, which is to say when $p$ and $q$ agree. But that is precisely the condition for $p\leftrightarrow q$. So $\sim (p\leftrightarrow \sim q)$ is equivalent to $p\leftrightarrow q$.