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

We need to find the negation of $$\sim p \wedge (p \vee q)$$.

Applying De Morgan's law, the negation is $$\sim(\sim p) \vee \sim(p \vee q)$$, which simplifies to $$p \vee (\sim p \wedge \sim q)$$.

Now we apply the distributive law: $$p \vee (\sim p \wedge \sim q) = (p \vee \sim p) \wedge (p \vee \sim q)$$.

Since $$p \vee \sim p$$ is always true (a tautology), this reduces to $$T \wedge (p \vee \sim q) = p \vee \sim q$$.

Therefore, the negation of $$\sim p \wedge (p \vee q)$$ is $$p \vee \sim q$$.