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

If ${(p \wedge \sim q) \wedge (p \wedge r)} \rightarrow (\sim p \vee q)$ has a truth value of $False$,then the truth values of the statements $p, q, r$ are respectively:

Among the two statements:
$(S1): (p \Rightarrow q) \wedge (q \wedge (\sim q))$ is a contradiction and
$(S2): (p \wedge q) \vee ((\sim p) \wedge q) \vee (p \wedge (\sim q)) \vee ((\sim p) \wedge (\sim q))$ is a tautology.

The negation of the contrapositive of the statement $(p \vee \sim q) \to (p \wedge \sim q)$ is

The simplified switching circuit for the following circuit is (Assume the circuit consists of two switches $S_1$ and $S_2$ in parallel, connected in series with a switch $S_3$):

$(p \wedge r) \Leftrightarrow (p \wedge (\sim q))$ is equivalent to $(\sim p)$ when $r$ is.