Final answer:
The board of directors of a nonprofit is fulfilling the duty of obedience when they assess whether a new program aligns with the organization's mission. This duty is one of the core responsibilities of board members alongside the duty of care and loyalty. Thus, the option D is the correct answer.
Step-by-step explanation:
The board of directors of a nonprofit debating, if a proposed new program aligns with the organization's mission, is applying the duty of obedience. This duty requires board members to ensure that the organization adheres to its stated mission and complies with all applicable laws and regulations. It's one of the core fiduciary duties that also include the duty of care and the duty of loyalty. The duty of care refers to the responsibility of board members to make informed decisions and exercise the same care an ordinarily prudent person would take under similar circumstances. The duty of loyalty requires board members to act in the organization's best interests, without personal conflict. By contrast, the duty of investment is not a widely recognized fiduciary duty in the context of nonprofit governance.