Truman made the decision to deploy the atomic bomb against Japan largely because of the

A.
importance of the Pacific theater to victory in Europe.

B.
concern about the cost in American lives of an invasion of Japan.

C.
desire to take revenge on Japan for their attack on Pearl Harbor.

D.
support he wanted to show troops fighting at Iwo Jima and Okinawa.

B. concern about the cost in American lives of an invasion of Japan.

The correct answer is B. concern about the cost in American lives of an invasion of Japan.

To determine the answer to this question, we need to analyze the reasons behind President Truman's decision to deploy the atomic bomb against Japan. It is important to note that this question is asking about the main factor behind Truman's decision.

A. Importance of the Pacific theater to victory in Europe - The Pacific theater was indeed important to the overall Allied victory in World War II, but it was not the primary reason for Truman's decision to use the atomic bomb.

B. Concern about the cost in American lives of an invasion of Japan - This factor played a significant role in Truman's decision. It was estimated that an invasion of Japan would result in a high number of casualties among American troops, potentially numbering in the hundreds of thousands. Truman wanted to avoid such large-scale loss of life.

C. Desire to take revenge on Japan for their attack on Pearl Harbor - While the attack on Pearl Harbor did create a sense of anger and desire for revenge among Americans, it was not the main reason for Truman's decision to use the atomic bomb.

D. Support he wanted to show troops fighting at Iwo Jima and Okinawa - While showing support to the troops was important to Truman, it was not the primary reason behind his decision to use the atomic bomb.

Therefore, the correct answer is B. Concern about the cost in American lives of an invasion of Japan. Truman's decision to deploy the atomic bomb was primarily driven by the potential loss of American lives that an invasion of Japan would entail.