The statement $p \rightarrow \sim q$ is false,if

The negation of the statement " $72$ is divisible by $2$ and $3$ " is

$(\sim (\sim p)) \wedge q$ is equal to .........

Which of the following statements is a tautology?

$(p \wedge \sim q) \wedge (\sim p \vee q)$ is

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