Final answer:
The claim that MHC I molecules only display viral peptides is false; they present both self-antigens and foreign antigens on the surface of all nucleated cells. MHC II molecules, however, are only found on antigen-presenting cells and are involved in presenting antigens to helper T-cells.
Step-by-step explanation:
The statement that MHC I molecules found at the surface of the cell display only peptides of viral origins is false. MHC I molecules are expressed on all nucleated cells and are essential for the presentation of normal "self" antigens as well as foreign antigens. When a cell becomes infected by an intracellular pathogen, such as a virus, it will also present viral antigens on MHC I, which are then recognized by cytotoxic T cells.
Hence, although MHC I can present viral peptides, they also present self-antigens as part of the normal cellular process. On the other hand, MHC II molecules are presented only on the surface of antigen-presenting cells (APCs) such as macrophages, dendritic cells, and B cells which are crucial for antigen presentation to helper T-cells (CD4+ T cells).