The statement pattern $(p \wedge q) \vee (\sim p \wedge q) \vee (r \wedge \sim q)$ is logically equivalent to:

Consider the statement patterns:
$A$. $(q \to p) \lor (p \to q)$
$B$. $(\sim p \lor \sim q) \leftrightarrow \sim (p \land q)$
$C$. $[(p \lor q) \land \sim p] \land \sim q$
$D$. $(p \land q) \land (\sim p \lor \sim q)$
Which of the following is true?

The negation of the conditional statement,"If it rains,$I$ shall go to school" is:

Which of the following statements is a contradiction?

The statement $(P$ $\Rightarrow Q) \wedge (R$ $\Rightarrow Q)$ is logically equivalent to:

The contrapositive of the inverse of $p$ $\rightarrow (p$ $\rightarrow q)$ is