Emperor Trajan is a great one
The correct answer to this open question is the following.
One goal of U.S involvement in the war in Afghanistan was to eliminate the terrorist cell led by Osama bin Laden, after this cell made itself responsible for the terrorist attacks of September 11, 2001.
One challenge of U.S involvement in the war in Afghanistan was that the Afghans knew their territory very well. That is why President Bush ordered an air raid over Afghanistan, with the support of Great Britain.
One goal of U.S involvement in the war in Irak was to capture and kill Irak's dictator Sadam Hussein. One challenge of U.S involvement in the war in Irak was to demonstrate that Sadam Hussein had arsenals of weapons of mass destruction. The US troops never find these weapons.
I think the correct answers from the choices are options first and the last option. Aristotle's definition of governments would be rule by a few called an aristocracy and rule by many called a democracy. Hope this answers the question. Have a nice day.