The output of the following circuit is

The negation of the inverse of the statement $\sim p \lor q$ is...

Which of the following statements is true?

If $p \rightarrow (p \wedge \neg q)$ is false,then the truth values of $p$ and $q$ are respectively

The correct logical equivalences from the following are:
$(I)$ $p \to (q \to r) \equiv (p \land q) \to r$
$(II)$ $(p \to q) \to r \equiv p \to (q \lor r)$
$(III)$ $(p \to q) \to r \equiv (p \to r) \land (\sim q \to r)$
$(IV)$ $p \to (q \to r) \equiv q \to (p \to r)$

Let $p$ and $q$ be two statements. Amongst the following,the statement that is equivalent to $p \to q$ is