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:

Rinzai School

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Wabi Aesthetic

A traditional Japanese aesthetic centered on the acceptance of transience and imperfection, characterized by simplicity, modesty, and appreciation of the organic nature of objects.

Tea Ceremony Utensils

Tools and items used in the traditional ritual of the Tea Ceremony, which varies in different cultures, notably Japanese (Chanoyu) or Chinese (Gongfucha).

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A significant form of art and industry in Vietnam, known for its unique styles, techniques, and history dating back several centuries, including both utilitarian and decorative items.