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

Which of the following statements is a tautology?

Let $F_{1}(A, B, C) = (A \wedge \sim B) \vee [\sim C \wedge (A \vee B)] \vee \sim A$ and $F_{2}(A, B) = (A \vee B) \vee (B \rightarrow \sim A)$ be two logical expressions. Then ...... .

Which of the following is the inverse of the proposition: "If a number is a prime then it is odd."

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

Let $a : \sim (p \wedge \sim r) \vee (\sim q \vee s)$ and $b : (p \vee s) \leftrightarrow (q \wedge r)$. If the truth values of $p$ and $q$ are true and that of $r$ and $s$ are false,then the truth values of $a$ and $b$ are respectively: