1. **State the problem:** Determine whether the logical formula $$((p \to n2) \lor (p \to q))$$ is a tautology, contingency, or contradiction. 2. **Recall definitions:** - A **tautology** is a formula that is true in every possible interpretation. - A **contradiction** (absurdity) is false in every interpretation. - A **contingency** is true in some interpretations and false in others. 3. **Analyze the formula:** The formula is $$((p \to n2) \lor (p \to q))$$. 4. **Note:** The symbol \(n2\) is unusual in propositional logic; assuming it is a propositional variable (like \(p\) or \(q\)). 5. **Recall implication equivalence:** $$p \to r \equiv \neg p \lor r$$ 6. **Rewrite each implication:** $$p \to n2 \equiv \neg p \lor n2$$ $$p \to q \equiv \neg p \lor q$$ 7. **Rewrite the whole formula:** $$((\neg p \lor n2) \lor (\neg p \lor q))$$ 8. **Simplify using associativity and idempotency:** $$\neg p \lor n2 \lor q$$ 9. **Interpretation:** The formula is true if \(\neg p\) is true, or \(n2\) is true, or \(q\) is true. 10. **Check if formula is always true:** - If \(p\) is true, then formula depends on \(n2 \lor q\). - If both \(n2\) and \(q\) are false, formula is false. 11. **Conclusion:** The formula is not always true (not a tautology). It is not always false (not a contradiction). Therefore, it is a **contingency**. **Final answer:** The formula $$((p \to n2) \lor (p \to q))$$ is a **contingency**.