1. **State the problem:** We want to analyze the logical argument $[(P \to Q) \wedge \neg P] \to P$ and determine its validity. 2. **Recall the implication formula:** An implication $A \to B$ is false only when $A$ is true and $B$ is false; otherwise, it is true. 3. **Analyze the antecedent:** The antecedent is $(P \to Q) \wedge \neg P$. 4. **Recall that $P \to Q$ is logically equivalent to $\neg P \vee Q$**. 5. **Substitute:** The antecedent becomes $(\neg P \vee Q) \wedge \neg P$. 6. **Simplify the antecedent:** Since $\neg P$ is true in the conjunction, the antecedent is true only if $\neg P$ is true. 7. **Evaluate the implication:** The whole statement is $[(P \to Q) \wedge \neg P] \to P$. 8. **If $\neg P$ is true, then $P$ is false, so the consequent $P$ is false.** 9. **Therefore, the implication is false when antecedent is true and consequent is false, which happens when $P$ is false and $\neg P$ is true.** 10. **Hence, the argument is not a tautology; it is false in some cases.** **Final answer:** The argument $[(P \to Q) \wedge \neg P] \to P$ is not valid (not a tautology).