$\sim[(p \vee \sim q) \rightarrow (p \wedge \sim q)] \equiv$

$\sim(\sim p \rightarrow q) \equiv$

The negation of the Boolean expression $((\sim q) \wedge p) \Rightarrow ((\sim p) \vee q)$ is logically equivalent to

If the truth value of the compound statement $[(p \leftrightarrow q) \land (q \to r) \land \sim r] \to (p \land \sim q)$ is false, then the truth values of the statement patterns $(p \to q) \leftrightarrow (q \to r)$ and $\sim (p \lor r) \to (q \land p)$ are, respectively ...

Consider the following three statements:
$(A)$ If $3+3=7$ then $4+3=8$.
$(B)$ If $5+3=8$ then earth is flat.
$(C)$ If both $(A)$ and $(B)$ are true then $5+6=17$.
Which of the following statements is correct?

Which of the following is false?