The contrapositive of the converse of $p \Rightarrow q$ is......

Which of the following is not logically equivalent to the proposition: "$A$ real number is either rational or irrational"?

Which of the following statement patterns is a contradiction?
$S_{1} \equiv (p \rightarrow q) \wedge (p \wedge \sim q)$
$S_{2} \equiv [p \wedge (p$ $\rightarrow q)]$ $\rightarrow q$
$S_{3} \equiv (p \vee q) \rightarrow \sim p$
$S_{4} \equiv [p \wedge (p \rightarrow q)] \leftrightarrow q$

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

If $p \rightarrow (q \vee r)$ is false,then what are the truth values of $p, q, r$ respectively?

The contrapositive of the statement pattern $[p \lor (p \to q)] \to (p \land \sim q)$ is