These statements would have been made towards the end of World War II. Specifically, these statements are referring to the United State's use of atomic bombs on Hiroshima and Nagasaki.
Speaker A is referring to the reason as to why Truman decided to drop these bombs. Truman felt that a land invasion of Japan would cause millions of casualties. Instead of dragging on the war a longer period of time, he felt that using these weapons would bring a quick end to the war.
Speaker B is referring to the other perspective, that Truman could have used the atomic bomb in a different way to ensure a surrender from Japan. This idea would have resulted in less deaths for Japan and possibly an unconditional surrender.
