A.I. Explanation:

Option 1: "Eating soy can protect against death from brain cancer."

Explanation: This option is incorrect because the text does not mention brain cancer as a specific health benefit associated with soybean products. Instead, it focuses on the reduction of risk from common killers such as heart attacks and strokes.

Option 2: "The Japanese live longer than the rest of us mostly because of soy products."

Explanation: While the text suggests that soybean products contribute to longevity, it does not claim that they are the 'mostly' responsible factor. The phrase 'many reasons' indicates that there are other factors involved in the longevity of Japanese people.

Option 3: "People who regularly ate tofu were 10 percent less likely to die from a common cause than those who avoided soy products."

Explanation: This option is correct as it directly reflects the information in the text, which states that those who regularly consumed tofu, natto, and miso were 10 percent less likely to die from common causes compared to those who did not consume soybean products.

Option 4: "Higher intake of fermented soy products was not associated with a lower risk of death."

Explanation: This option contradicts the text, which clearly states that a higher intake of fermented soy products was associated with a lower risk of mortality. Therefore, this statement is false.