Subjects logic

Tautology Contingency

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Tautology Contingency


1. **Stating the problem:** Determine whether the logical statement $$(P \to Q) \lor (P \to Q)$$ is a tautology, contingency, or contradiction. 2. **Recall definitions:** - A **tautology** is a statement that is always true regardless of the truth values of its components. - A **contradiction** (absurdity) is always false. - A **contingency** is sometimes true and sometimes false. 3. **Analyze the statement:** The statement is $$(P \to Q) \lor (P \to Q)$$ which simplifies to $$(P \to Q)$$ because the disjunction of a statement with itself is just the statement. 4. **Recall implication truth table:** $$P \to Q$$ is false only when $P$ is true and $Q$ is false; otherwise, it is true. 5. **Conclusion:** Since $$(P \to Q)$$ is not always true nor always false, it is a **contingency**. **Final answer:** The statement $$(P \to Q) \lor (P \to Q)$$ is a **contingency**.