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

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

Transcript text: 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? \[ N \supset A \] N A Select one: a. $\mathrm{N}: \mathrm{T}$ A: T b. $\mathrm{N}: \mathrm{T}$ A: F c. $N: F \quad A: T$ d. None-the argument is valid. e. $N: F$ A: F

Solution

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.

Step 1: Evaluate the Implication

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} $

Step 2: Identify the Invalid Option

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} $.