Final answer:
President Truman did not seek a formal declaration of war from Congress during the Korean War, instead responding to North Korea's aggression with U.S. military support under UN authorization.
Step-by-step explanation:
The correct statement about the Korean War is that President Truman never asked Congress for a formal declaration of war. While the United Nations did authorize the use of force to stop North Korea, the Soviet Union supported North Korea but did not send troops, and South Korea did not surrender even after China joined the conflict. Truman's decision to commit U.S. forces to support South Korea was made with the rationale of containing the spread of communism, upholding U.S. credibility, and preventing the Domino Theory from playing out in Asia.