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

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

Consider statements $p: S_1$ is closed; $q: S_2$ is closed; $r: S_3$ is closed. The simplified equivalent circuit diagram and its logical statement for the switching circuit is respectively.

The negation of the statement $p \rightarrow (q \wedge r)$ is equal to .........

Check whether "Or" used in the following compound statement is exclusive or inclusive? Write the component statements of the compound statements and use them to check whether the compound statement is true or not. Justify your answer.
$t:$ You are wet when it rains or you are in a river.

The statement pattern $p$ $\rightarrow (q$ $\rightarrow p)$ is equivalent to