1. **State the problem:** We want to verify the logical argument: "If a number is even, then it is divisible by 2. The number is not divisible by 2. Therefore, the number is not even." using a truth table. 2. **Identify propositions:** Let $p$ = "The number is even" and $q$ = "The number is divisible by 2". 3. **Logical form:** The statement is $p \to q$. The argument is: - Premise 1: $p \to q$ - Premise 2: $\neg q$ - Conclusion: $\therefore \neg p$ 4. **Truth table setup:** We list all possible truth values for $p$ and $q$, then evaluate $p \to q$, $\neg q$, and $\neg p$. | $p$ | $q$ | $p \to q$ | $\neg q$ | $\neg p$ | |-----|-----|-----------|----------|----------| | T | T | T | F | F | | T | F | F | T | F | | F | T | T | F | T | | F | F | T | T | T | 5. **Check validity:** The argument is valid if whenever $p \to q$ is true and $\neg q$ is true, then $\neg p$ is also true. 6. **Analyze rows where $p \to q$ and $\neg q$ are true:** - Row 2: $p \to q$ is F, so ignore. - Row 4: $p \to q$ is T, $\neg q$ is T, and $\neg p$ is T. 7. **Conclusion:** In all cases where the premises are true, the conclusion is true. Therefore, the argument is logically valid. **Final answer:** The argument "If a number is even, then it is divisible by 2. The number is not divisible by 2. Therefore, the number is not even." is valid by truth table analysis.