**Core Concept**
The mandibular nerve, a branch of the trigeminal nerve (**cranial nerve V**), is responsible for sensory and motor functions in the lower face. It supplies various structures, including muscles of mastication and areas of the skin.

**Why the Correct Answer is Right**
To answer this question, one must identify which option is not supplied by the mandibular nerve. The mandibular nerve provides sensory innervation to the lower face, including the skin of the chin and the lower lip, and motor innervation to the muscles of mastication (**masseter, temporalis, medial pterygoid, and lateral pterygoid**).

**Why Each Wrong Option is Incorrect**
**Option A:** Incorrect because the mandibular nerve does supply the skin of the chin.
**Option B:** Incorrect because it also supplies the lower lip.
**Option C:** Incorrect as it supplies the anterior two-thirds of the tongue for non-taste sensation.

**Clinical Pearl / High-Yield Fact**
The mandibular nerve is crucial for controlling the muscles of mastication and providing sensation to the lower face. Damage can lead to difficulties in chewing and sensory loss.

**Correct Answer:** D.