The negative of the statement $\sim p \wedge (p \vee q)$ is

The expression $((p \wedge q) \vee (p \vee \sim q)) \wedge (\sim p \wedge \sim q)$ is equivalent to

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

Which of the following is a statement?

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?

If $p$: switch $S_1$ is closed,$q$: switch $S_2$ is closed,$r$: switch $S_3$ is closed,then the symbolic form of the following switching circuit is equivalent to: