Autoimmune diseases are those in which the Immune System can't differ the healthy and normal cells from the pathogens that could be causing diseases. The result is that the Immune System ends up attacking the body, instead of attacking a specific disease.
An antigen is what stimulates a immune response, activating the white blood cells (leukocytes), which will fight the disease. It can be present in bacterias, viruses and other pathogens. But, in autoimmune diseases, the Immune System attacks antigens that are present in healthy cells from the organism, causing an immune response.
So, the antigens are what triggers the immune response, they are not how the diseases are inherited (they are what triggers the response, but not how the disease is inherited), therefore a) is incorrect.
They are not responsible for destroying the body cells, they trigger this reaction but leukocytes are responsile for destroying the cells that are identified as a threat, So c) is also wrong.
They do not destroy the immune system as well. Some diseases may weaken the |mmune System enough so it barely works, leaving the body unprotected, but even on this cases the antigen is always the thing that triggers the immune response, not the response itself, so d) is also incorrect.
As the role of the antigens is to stimulate the immune response, the correct answer is b) they cause an immune response.