Questions: Use a truth table to answer the following question. Which, if any, set of truth values assigned to the atomic sentences shows that the following argument is invalid? N implies A N A Select one: a. N: T A: T b. N: T A: F c. N: F A: T d. None-the argument is valid. e. N: F A: F

Solution Steps

To determine if the argument $N \supset A$ is invalid, we need to find a set of truth values for $N$ and $A$ such that the premise $N \supset A$ is true, but the conclusion is false. In logical terms, an implication $N \supset A$ is false only when $N$ is true and $A$ is false. We will evaluate each option to see if it satisfies this condition.

We need to evaluate the implication $N \supset A$. The implication is defined as false only when $N$ is true and $A$ is false. Thus, we can summarize the truth values for the options provided:

• Option a: $N = \text{T}, A = \text{T}$ → $N \supset A = \text{T}$
• Option b: $N = \text{T}, A = \text{F}$ → $N \supset A = \text{F}$
• Option c: $N = \text{F}, A = \text{T}$ → $N \supset A = \text{T}$
• Option d: None (the argument is valid)
• Option e: $N = \text{F}, A = \text{F}$ → $N \supset A = \text{T}$

From the evaluation, we see that the only option that makes the implication $N \supset A$ false is option b, where $N = \text{T}$ and $A = \text{F}$.

Final Answer