Final answer:
The correct word to describe the student's action of giving up their seat to an elderly lady on the bus is 'offered', as it is the term that best captures the voluntary and considerate nature of the act.
Step-by-step explanation:
When considering the context in which one of the students gave up their seat to an elderly lady on the bus, the most appropriate word to define the student's action is offered. This is true because in everyday English, to offer one's seat to someone else implies a voluntary and considerate act of giving up something of value to oneself for another's comfort. Although 'yielded,' 'reserved,' and 'relinquished' could all refer to giving up a seat, 'offered' most accurately captures the courteous and proactive aspect of the student's behavior. 'Yielded' tends to imply giving way to another's demand or authority, 'relinquished' generally conveys a more formal relinquishment of possession or right, and 'reserved' is incorrect in this context as it usually means to keep or set aside for a specific purpose or use. The student offered the seat to the elderly lady, which would be the most appropriate and polite term to describe this action.