The two examples which correctly punctuate an essential expression or element in the sentence are:
Architecture, so popular with Native Americans, is still a flourishing art.
Mexico, where sports are popular, has hosted the Olympic Games at the World Cup.
Some constituents that alter a sentence are indispensable and restrict the meaning of an altered word or prhase, whereas others aren't indispensable and don't affect its meaning. The first ones are separated from the main idea using commas.
Mexico City is home to several museums that display the country’s past. Here we don't have any non essential element.
The National Historical Museum, which is in Chapultepec Castle, is concerned with Mexico’s history since the Spanish conquest. Here, information can't be ommited and in fact, shouldn't be set off with comas, since such expression contains essential information (it is not any National Historic Museum but the National Historic Museum which is in Chapultepec Castle).
Answer:
B. John was accepted for the program, but Bill was not.
At the end of Sophocles' Oedipus Rex, the protagonist Oedipus has gouged out his own eyes and is sent into exile. His wife (and -- spoiler alert -- his mother) is dead, having hung herself.
