**Core Concept**
The sphenoidal air sinus is one of the paranasal sinuses, and its innervation is crucial for understanding the sensory and autonomic nervous system's involvement in sinus pathology. The sphenoidal sinus is located within the body of the sphenoid bone, in close proximity to the pituitary gland.

**Why the Correct Answer is Right**
The sphenoidal sinus is supplied by the anterior branch of the maxillary nerve, which is a division of the trigeminal nerve (cranial nerve V). The maxillary nerve provides sensory innervation to the sphenoidal sinus, as well as the surrounding structures, including the nasal cavity and the palate. This innervation is essential for the sensation of pain, temperature, and touch in the sphenoidal sinus area.

**Why Each Wrong Option is Incorrect**
**Option A:** The ophthalmic nerve (cranial nerve V1) primarily supplies the eye and the surrounding orbital structures, not the sphenoidal sinus.
**Option B:** The mandibular nerve (cranial nerve V3) supplies the lower face, including the jaw, but not the sphenoidal sinus.
**Option C:** The facial nerve (cranial nerve VII) is responsible for facial expressions, taste, and the innervation of the salivary and lacrimal glands, but not the sphenoidal sinus.

**Clinical Pearl / High-Yield Fact**
The trigeminal nerve is a crucial structure in the assessment of facial pain, particularly in conditions like trigeminal neuralgia. Understanding the innervation of the sphenoidal sinus is essential for diagnosing and managing sinus-related pain and other neurological disorders.

**Correct Answer:** C. The mandibular nerve is incorrect, the correct answer should be A. The maxillary nerve.