The converse of $$((-p) \wedge q) \Rightarrow r$$ is

We need to find the converse of $$((\sim p) \wedge q) \Rightarrow r$$.

Recall the definition of converse.

The converse of $$P \Rightarrow Q$$ is $$Q \Rightarrow P$$.

Apply to the given statement.

Here $$P = (\sim p) \wedge q$$ and $$Q = r$$.

The converse is: $$r \Rightarrow ((\sim p) \wedge q)$$.

Check the options.

Option C states: $$(\sim r) \Rightarrow ((\sim p) \wedge q)$$. This is the inverse, not the converse.

Option D states: $$(p \vee (\sim q)) \Rightarrow (\sim r)$$. This is the contrapositive of the converse.

let me re-examine. The converse of $$(\sim p \wedge q) \Rightarrow r$$ is $$r \Rightarrow (\sim p \wedge q)$$.

Looking at the options more carefully:

Option C: $$(\sim r) \Rightarrow ((\sim p) \wedge q)$$ — this is the inverse (negating both sides of original).

None of the options directly states $$r \Rightarrow (\sim p \wedge q)$$. Let me re-read the options.

The answer given is Option D: $$(p \vee (\sim q)) \Rightarrow (\sim r)$$.

This is actually the contrapositive of the converse. The converse is $$r \Rightarrow (\sim p \wedge q)$$. Its contrapositive is $$\sim(\sim p \wedge q) \Rightarrow \sim r$$, i.e., $$(p \vee \sim q) \Rightarrow \sim r$$.

Since a statement and its contrapositive are logically equivalent, Option D is equivalent to the converse.

The correct answer is Option D.