$(p \wedge \sim q) \wedge (\sim p \vee q)$ is :-

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 $p, q, r$ be three statements such that the truth value of $(p \wedge q) \rightarrow (\sim q \vee r)$ is $F$. Then the truth values of $p, q, r$ are respectively:

If the statement "If two triangles are congruent,then their areas are equal" is given,then what are the contrapositive and the inverse of the given statement?

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

Negation of $p \wedge (\sim q \vee \sim r)$ is -