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

The contrapositive of a conditional statement $X \to Y$ is logically equivalent to the statement itself.

Therefore, the negation of the contrapositive of $X \to Y$ is logically equivalent to the negation of $X \to Y$.

The negation of $X \to Y$ is $X \wedge \sim Y$.

Given the statement $(p \vee \sim q) \to (p \wedge \sim q)$, we have $X = p \vee \sim q$ and $Y = p \wedge \sim q$.

The negation of the statement is:

$X \wedge \sim Y = (p \vee \sim q) \wedge \sim (p \wedge \sim q)$

By De Morgan's laws, $\sim (p \wedge \sim q) \equiv \sim p \vee q$.

Substituting this back, we get:

$(p \vee \sim q) \wedge (\sim p \vee q)$

Rearranging the terms, this is identical to $(\sim p \vee q) \wedge (p \vee \sim q)$.