The negation of the contrapositive of the statement pattern $(p \vee \sim q) \rightarrow (p \wedge \sim q)$ 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 $S_3$):

Negation of the inverse of the following statement pattern $(p \wedge q) \rightarrow (p \vee \sim q)$ is

If truth values of statements $p, q$ are true,and $r, s$ are false,then the truth values of the following statement patterns are respectively:
$a: \sim(p \wedge \sim r) \vee(\sim q \vee s)$
$b: (\sim q \wedge \sim r) \leftrightarrow(p \vee s)$
$c: (\sim p \vee q) \rightarrow(r \wedge \sim s)$

Consider the two statements:
$(S1): (p$ $\rightarrow q) \vee (\sim q$ $\rightarrow p)$ is a tautology.
$(S2): (p \wedge \sim q) \wedge (\sim p \vee q)$ is a fallacy.
Then:

Show that the statement $p:$ 'If $x$ is a real number such that $x^{3}+4x=0$,then $x$ is $0$' is true by the method of contrapositive.