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:

Total Utility

The complete satisfaction or advantage gained from consuming a specified overall amount of a product or service.

Utility-Maximizing

A principle of economics that assumes consumers aim to achieve the highest level of satisfaction possible from their available resources.

Total Product Curve

A graph that shows the relationship between the quantity of inputs used in production and the quantity of output generated, illustrating how output changes with input variations.

Marginal Cost Curve

The marginal cost curve illustrates how the expense of producing one additional unit of a good changes as more goods are produced, typically upward sloping due to increasing costs.