Final answer:
The United States did not go to war with China over the Korea problem.
Step-by-step explanation:
False. The United States did not go to war with China over the Korea problem. The United States and China were involved in the Korean War, which took place from 1950 to 1953. The war was primarily fought between North Korea (supported by China and the Soviet Union) and South Korea (supported by the United States and other United Nations forces). Although China was involved in the conflict, it did not lead to a direct war between the United States and China.
Learn more about US and China involvement in the Korean War