**Core Concept**
The question is testing the student's ability to differentiate between various types of chronic lymphocytic leukemias (CLL) and other conditions based on their peripheral blood smear characteristics. CLL is a malignancy characterized by the clonal expansion of mature, often functionally incompetent, lymphocytes.

**Why the Correct Answer is Right**
The presence of 80% lymphocytes on the peripheral smear, with a predominance of mature lymphocytes, is suggestive of CLL. The presence of 20% polymorphonuclear cells (PMNs) is a common finding in CLL, as these patients often have a mild leukocytosis. The absolute lymphocyte count in CLL is typically elevated, and the lymphocytes are often mature with a mature morphology. In CLL, the lymphocytes are usually CD5+ and CD23+, which is not mentioned in the question, but the clinical presentation and peripheral smear characteristics are consistent with CLL.

**Why Each Wrong Option is Incorrect**
**Option A:** HIV is a viral infection that can lead to immunosuppression and lymphadenopathy, but it typically presents with a lower lymphocyte count and a variety of other clinical findings, such as fever, weight loss, and opportunistic infections.

**Option B:** CML (Chronic Myeloid Leukemia) is a myeloproliferative disorder characterized by the clonal expansion of myeloid cells, often with an elevated white blood cell count and the presence of the Philadelphia chromosome. The peripheral smear in CML typically shows a predominance of myeloid cells, not lymphocytes.

**Option D:** TB (Tuberculosis) is a bacterial infection that can cause lymphadenopathy and immunosuppression, but it typically presents with a variety of other clinical findings, such as fever, weight loss, and respiratory symptoms.

**Clinical Pearl / High-Yield Fact**
It's essential to remember that CLL can present with a wide range of clinical findings, from asymptomatic to symptomatic, and that the diagnosis should be based on a combination of clinical findings, laboratory results, and bone marrow examination.

**✓ Correct Answer: C. CLL**