The correct answer is true.
It is true that although male citizens have to enroll in the selective service, the draft has not been used since 1973.
After the Vietnam War and the many social protests from the American citizens by the deaths of American soldiers in the war, the draft has not been used. After the draft, young Americans have to register, although the participation in the military forces is voluntary. In April 1975, the registration requirement was ended but President Jimmy Carter resumed it in 1980 as a prevention to the Soviet Union invasion of Afghanistan. The registration is still in place.