Final answer:
Legal aliens in the United States are permitted to study at an American school, but they cannot vote, serve jury duty, or become mayor. These privileges are reserved for U.S. citizens.
Step-by-step explanation:
The legal rights that the United States provides to legal aliens include living and working anywhere in the U.S., attending public schools, joining the armed forces, and qualifying for some Social Security benefits. Of the options given in the question, legal aliens are given permission to study at an American school. They are not, however, allowed to vote, serve jury duty, or become mayor as these rights are reserved for U.S. citizens.
Voting is a right that is only for U.S. citizens in Federal elections and in most state and local elections as well. Serving on a jury or holding the public office of mayor, also typically require citizenship. Therefore, those who are permanent residents but not citizens are unable to participate in these activities.
It is important to know how people can become citizens if they are not born in the U.S. or don't have automatic citizenship through their parents. This process involves having knowledge of U.S. government and history, and being willing and able to take the Oath of Allegiance.