The negation of the expression $$q \vee ((\sim q) \wedge p)$$ is equivalent to

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

First, let us simplify the expression using the distributive law:

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

Since $$q \vee \sim q = T$$ (tautology):

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

Now, the negation is:

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

This follows from De Morgan's law: $$\sim(A \vee B) = (\sim A) \wedge (\sim B)$$.

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