1. The problem asks to verify if the logical statement $\neg q \lor (p \to q)$ is a tautology. 2. Recall the implication equivalence: $p \to q$ is logically equivalent to $\neg p \lor q$. 3. Substitute this into the original expression: $$\neg q \lor (p \to q) = \neg q \lor (\neg p \lor q)$$ 4. By associativity and commutativity of $\lor$, rearrange terms: $$\neg q \lor q \lor \neg p$$ 5. Note that $\neg q \lor q$ is a tautology (always true), denoted as $T$: $$T \lor \neg p$$ 6. Since $T \lor \neg p = T$ (true or anything is true), the entire expression is always true. 7. Therefore, $\neg q \lor (p \to q)$ is indeed a tautology. This confirms the correctness of the given statement.