What disease, caused by HIV, disables the immune response by destroying important white blood cells?

The disease caused by HIV that disables the immune response by destroying important white blood cells is AIDS, which stands for Acquired Immunodeficiency Syndrome. HIV attacks the body's immune system, specifically targeting CD4 cells, which are crucial for the immune response. As the number of these cells decreases due to the ongoing infection, the body becomes increasingly vulnerable to opportunistic infections and certain cancers. This progressive immune system deterioration is what characterizes AIDS.

In contrast, other options do not align with the mechanism or causative agent of the disease at hand. Autoimmune Deficiency Syndrome is not a recognized medical term; cancer encompasses a broad range of diseases characterized by uncontrolled cell growth, not linked to HIV specifically; and Multiple Sclerosis is a neurological condition that affects the central nervous system rather than the immune system's response to infections. Thus, AIDS is clearly the correct answer based on its direct relationship with HIV and its significant impact on the immune system.