Final answer:
The nucleus ambiguus is associated with the motor functions of cranial nerves IX, X, and partially XI, which are involved in swallowing, phonation, and muscle control.
Step-by-step explanation:
The nucleus ambiguus contributes to the motor component of several cranial nerves, specifically CN IX (glossopharyngeal nerve), CN X (vagus nerve), and partially to CN XI (spinal accessory nerve). These nerves are responsible for a variety of functions, including swallowing, phonation, and controlling the sternocleidomastoid and trapezius muscles. The pneumonic 'Some Say Marry Money But My Brother Says Brains Beauty Matter More' is often used to remember the basic functions of the cranial nerves; in this case, CN IX and CN X have both sensory and motor components, while CN XI is primarily motor.