The statement pattern $(p \wedge q) \wedge [\sim r \vee (p \wedge q)] \vee (\sim p \wedge q)$ is equivalent to $......$

Write the negation of the following statement:
Both the diagonals of a rectangle have the same length.

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

The dual of the statement pattern $(p \land \sim q) \to (q \land \sim p)$ is equivalent to

If the truth value of the statement pattern $( \sim p \land q) \lor ( \sim p \land \sim q) \lor (p \land \sim q)$ is $F$, then the truth values of $(p \lor \sim q)$ and $(p \to q)$ are ... respectively.

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: