Final answer:
The olfactory nerve (D) does not play a role in swallowing, unlike the glossopharyngeal, hypoglossal, and vagus nerves, which are all involved in the swallowing process.
Step-by-step explanation:
The nerve that does NOT play a role in swallowing is the olfactory nerve (D). The olfactory nerve is responsible for the sense of smell and does not participate in the swallowing process. In contrast, the glossopharyngeal (A), hypoglossal (B), and vagus (C) nerves do play roles in swallowing. The glossopharyngeal nerve is involved in taste and the gag reflex, the hypoglossal nerve controls movements of the tongue, and the vagus nerve stimulates the contraction of skeletal muscles in the pharynx and larynx aiding in swallowing.