The correct answer is: Only argument II is strong.
Argument I is weak because it does not provide any evidence to support its claim that the United Nations has no role to play in the absence of the Cold War. The Cold War was a period of tension and hostility between the United States and the Soviet Union, and it is true that the United Nations played a significant role in managing that conflict. However, the United Nations has also played a role in many other conflicts, both before and after the Cold War. For example, the United Nations has been involved in peacekeeping missions in countries such as Bosnia, Kosovo, and Lebanon. It has also provided humanitarian assistance to countries affected by natural disasters and armed conflict. Therefore, there is no evidence to suggest that the United Nations has no role to play in the absence of the Cold War.
Argument II is strong because it provides evidence to support its claim that the United Nations is necessary to prevent world war. The argument states that in the absence of the United Nations, there may be a world war. This is a plausible claim, as the United Nations has played a significant role in preventing war since its founding in 1945. For example, the United Nations was instrumental in preventing a war between India and Pakistan over Kashmir in 1947. It has also played a role in preventing wars between other countries, such as Iran and Iraq. Therefore, there is evidence to suggest that the United Nations is necessary to prevent world war.