Determine Whether the Following Argument Is Valid or Invalid

question 20

Essay

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.

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Definitions:

Definition

A statement that describes the essence, precise meaning, or scope of a word or phrase.

Institutions

Organizations or establishments founded for a specific purpose, often societal, such as educational, religious, or financial entities.

Frail Elderly

Older adults who are in a weakened physical condition, often leading to increased vulnerability to health complications and dependence on others.

Dementia

Dementia is a general term for a decline in mental ability severe enough to interfere with daily life, characterized by deterioration in memory, thinking, behavior, and the ability to perform everyday activities.