Determine whether the following argument is valid or invalid. Include a truth table and a few words explaining why the truth table shows validity or invalidity.
If 12 divides 709,438 then 3 divides 709,438.
If the sum of the digits of 709,438 is divisible by 9 then 3 divides 709,438.
The sum of the digits of 709,438 is not divisible by 9.
Therefore, 12 does not divide 709,438.

Question

Quizplus · Accepted Answer

The Answer is Let p be "12 divides 709,438," q be "3 divides 709,438," and r be "The sum of the digits of 709,438 is
divisible by 9." Then the given argument has the following form:

p ightarrow q

\begin{array} { l } r ightarrow q \\sim r\end{array}

Therefore

\sim p

.
$Let p be 12 divides 709,438, q be 3 divides 709,438, and r be The sum of the digits of 709,438 is divisible by 9. Then the given argument has the following form: p ightarrow q \begin{array} { l } r ightarrow q \ \sim r \end{array} Therefore \sim p . Row 2 of the truth table shows that it is possible for an argument of this form to have true premises and a false conclusion. Therefore, the given argument is invalid.$ Row 2 of the truth table shows that it is possible for an argument of this form to have true premises and a false conclusion. Therefore, the given argument is invalid.

Determine Whether the Following Argument Is Valid or Invalid