1. **State the problem:** Verify whether the statement $$\sim(\sim q \to p) \to \sim q$$ is a tautology using the laws of logic. 2. **Recall the implication equivalence:** An implication $$A \to B$$ is logically equivalent to $$\sim A \lor B$$. 3. **Rewrite the inner implication:** $$\sim q \to p$$ is equivalent to $$\sim(\sim q) \lor p$$ which simplifies to $$q \lor p$$. 4. **Apply negation to the inner implication:** $$\sim(\sim q \to p) = \sim(q \lor p)$$. 5. **Use De Morgan's law:** $$\sim(q \lor p) = \sim q \land \sim p$$. 6. **Rewrite the original statement:** $$\sim(\sim q \to p) \to \sim q$$ becomes $$(\sim q \land \sim p) \to \sim q$$. 7. **Rewrite the implication again:** $$(\sim q \land \sim p) \to \sim q$$ is equivalent to $$\sim(\sim q \land \sim p) \lor \sim q$$. 8. **Apply De Morgan's law to the negation:** $$\sim(\sim q \land \sim p) = q \lor p$$. 9. **Substitute back:** $$q \lor p \lor \sim q$$. 10. **Simplify:** $$q \lor \sim q \lor p$$. 11. **Recognize the tautology:** $$q \lor \sim q$$ is always true, so the entire expression is always true regardless of $$p$$. **Final conclusion:** The statement $$\sim(\sim q \to p) \to \sim q$$ is a tautology.