The negation of the statement pattern $\sim s \vee (\sim r \wedge s)$ is equivalent to

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:

If $p$: The total prime numbers between $2$ to $100$ are $26$.
$q$: Zero is a complex number.
$r$: Least common multiple ($L$.$C$.$M$.) of $6$ and $7$ is $6$.
Then which of the following is correct?

State the converse and contrapositive of the following statement:
$r:$ If it is hot outside,then you feel thirsty.

Which of the following statement patterns is a tautology?
$S_1 \equiv (\sim q \wedge p) \wedge q$
$S_2 \equiv [p \wedge (p$ $\rightarrow q)]$ $\rightarrow q$
$S_3 \equiv (p \wedge q) \wedge (\sim p \vee \sim q)$
$S_4 \equiv (p \wedge q) \rightarrow r$

For each of the following compound statements,first identify the connecting words and then break it into component statements.
All rational numbers are real and all real numbers are not complex.