Step 1: The task.
We pick the true statements about the immune system.
Step 2: Statement I, memory B-cells.
After the first exposure to a germ, some B-cells become memory cells. If the same germ comes again, they act fast and strong, giving a quick secondary response. This statement is true.
Step 3: Statement II, complement system.
Complement proteins do float in blood plasma, but they belong to innate (inborn) immunity, not adaptive immunity. So saying they are part of adaptive immunity is wrong.
Step 4: Statement III, cell mediated immunity.
Cell mediated immunity is mainly the work of cytotoxic T-cells, which kill infected cells directly. This statement is true.
Step 5: Statement IV, plasma cells.
Plasma cells are antibody factories. They release antibodies but they do not crawl around eating germs. Phagocytosis is done by cells like macrophages. So this statement is wrong.
Step 6: Conclusion.
Only I and III are correct, so the answer is "I and III". \[ \boxed{\text{I and III}} \]