$\sim (p \vee (\sim q))$ is equal to .......

Statement-$1$: $\sim (p \Leftrightarrow \sim q)$ is equivalent to $p \Leftrightarrow q$.
Statement-$2$: $\sim (p \Leftrightarrow \sim q)$ is a tautology.

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

If the symbolic form of the switching circuit is $[\sim p \vee (p \wedge \sim q)] \vee q$,then the current flows through the circuit only if

Write the contrapositive and converse of the following statement:
If $x$ is a prime number,then $x$ is odd.

The negation of $q \vee \sim (p \wedge r)$ is