What cranial nerve is not in involved either taste or smell?

Olfaction is the sense of smell, and gustation is the sense of taste. The cranial nerves involved in taste and smell are:

Olfactory Nerve (cranial nerve I): responsible for smell.

Facial Nerve (cranial nerve VII): responsible for taste in the anterior two-thirds of the tongue.

Glossopharyngeal Nerve (cranial nerve IX): responsible for taste in the posterior third of the tongue.

Vagus Nerve (cranial nerve X): responsible for taste in the epiglottis and a small area of the pharynx.

The only cranial nerve not involved in either taste or smell is the Accessory nerve (cranial nerve XI). This nerve controls the sternocleidomastoid and trapezius muscles, which are involved in head and neck movement.