Step 1: Understanding neoplasms in AIDS patients. Patients with AIDS are highly immunocompromised due to the depletion of CD4+ T cells. This increases their susceptibility to certain cancers, especially those caused by viral infections.
Step 2: Explanation of Kaposi sarcoma. Kaposi sarcoma is a vascular tumor caused by human herpesvirus-8 (HHV-8). It is the most common neoplasm in AIDS patients and presents as red or purple skin lesions, often involving mucous membranes, lymph nodes, and visceral organs.
Step 3: Comparison with other options.
- Option \( (A) \): Carcinoma of the breast is not associated with AIDS.
- Option \( (B) \): Acute myeloid leukemia (AML) is unrelated to AIDS.
- Option \( (C) \): Adenocarcinomas are less common in AIDS patients compared to Kaposi sarcoma.
Conclusion: Kaposi sarcoma is the most common neoplasm in AIDS patients, making \( (D) \) the correct answer.