Does the sentence "The Western emperor Gratian refused the office of pontifex maximus, and against the protests of the senate, removed the altar of Victory from the senate house and began the disestablishment of the Vestals." provide a valid answer to the question "What office did Western emperor Gratian decline?"

A: yes

Does the sentence "Internationally, the torch and its accompanying party traveled in a chartered Air China Airbus A330 (registered B-6075), painted in the red and yellow colors of the Olympic Games." provide a valid answer to the question "What color was the chartered plane?"

A: yes

Does the sentence "For example, a natural science like astronomy was only studied (if at all) to supply religious needs, like the time for prayer." provide a valid answer to the question "What was the purpose of studying natural sciences in madaris?"

A: yes

Does the sentence "During the early High Middle Ages, Germany was ruled by the Ottonian dynasty, which struggled to control the powerful dukes ruling over territorial duchies tracing back to the Migration period." provide a valid answer to the question "What dynasty controlled Germany in the early High Middle Ages?"

A:
yes