When a person tests positive for HIV it is not a test for the virus itself but for antibodies to the virus and the test is not able to distinguish between HIV antibodies and a multitude of other antibodies. Many conditions can lead to a false positive result including flu shots hepatitis and pregnancy.
A social problem is one that concerns the way in which people live together in one society. A racial problem is a problem which confronts two different races who live in two separate societies even if those societies are side by side.