Negation of the Boolean statement $$(p \vee q) \Rightarrow ((\sim r) \vee p)$$ is equivalent to:

We need to find the negation of $$(p \vee q) \Rightarrow ((\sim r) \vee p)$$. The negation of $$A \Rightarrow B$$ is $$A \wedge (\sim B)$$. Here $$A = (p \vee q)$$ and $$B = ((\sim r) \vee p)$$, so its negation is $$(p \vee q) \wedge \sim((\sim r) \vee p)$$.

By De Morgan's law, $$\sim((\sim r) \vee p) = r \wedge (\sim p)$$, therefore the expression becomes $$(p \vee q) \wedge r \wedge (\sim p)$$. Since $$\sim p$$ holds, $$(p \vee q) \wedge (\sim p)$$ simplifies to $$q \wedge (\sim p)$$, giving $$(\sim p) \wedge q \wedge r$$.

Therefore, the answer is Option C: $$(\sim p) \wedge q \wedge r$$.